Towards a Lie theory of locally convex groups

A. Abouqateb and K.-H. Neeb, Integration of locally exponential Lie algebras of vector fields, submitted. M. Adams, T. Ratiu and R. Schmid, The Lie group structure of diffeomorphism groups and invertible Fourier integral operators, with applications, In: Infinite-dimensional groups with applications, Berkeley, Calif., 1984, Math. Sci. Res. Inst. Publ., 4, Springer-Verlag, 1985, pp. 1–69. M. Adams, T. Ratiu and R. Schmid, A Lie group structure for pseudodifferential operators, Math. Ann., 273 (1986), 529–551. M. Adams, T. Ratiu and R. Schmid, A Lie group structure for Fourier integral operators, Math. Ann., 276 (1986), 19–41. I. Ado, Über die Darstellung von Lieschen Gruppen durch lineare Substitutionen, Bull. Soc. Phys. Math. Kazan (3), 7 (1936), 3–43. S. A. Albeverio, R. J. Høegh-Krohn, J. A. Marion, D. H. Testard and B. S. Torrésani, Noncommutative distributions. Unitary representation of Gauge Groups and Algebras, Monogr. Textbooks Pure Appl. Math., 175, Marcel Dekker, Inc., New York, 1993. G. R. Allan, A spectral theory for locally convex algebras, Proc. London Math. Soc. (3), 15 (1965), 399–421. B. N. Allison, S. Azam, S. Berman, Y. Gao and A. Pianzola, Extended Affine Lie Algebras and Their Root Systems, Mem. Amer. Math. Soc., 603, Providence, R.I., 1997. B. Allison, G. Benkart and Y. Gao, Central extensions of Lie algebras graded by finite-root systems, Math. Ann., 316 (2000), 499–527. I. Amemiya, Lie algebra of vector fields and complex structure, J. Math. Soc. Japan, 27 (1975), 545–549. V. I. Arnold, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits, Ann. Inst. Fourier, 16 (1966), 319–361. V. I. Arnold and B. A. Khesin, Topological Methods in Hydrodynamics, Springer-Verlag, 1998. J. A. de Azcarraga and J. M. Izquierdo, Lie Groups, Lie Algebras, Cohomology and some Applications in Physics, Cambridge Monogr. Math. Phys., 1995. H. F. Baker, On the exponential theorem for a simply transitive continuous group, and the calculation of the finite equations from the constants of structure, J. London Math. Soc., 34 (1901), 91–127. H. F. Baker, On the calculation of the finite equations of a continuous group, Lond. M. S. Proc., 35 (1903), 332–333. A. Banyaga, The Structure of Classical Diffeomorphism Groups, Kluwer Academic Publishers, 1997. A. Bastiani, Applications différentiables et variétés différentiables de dimension infinie, J. Anal. Math., 13 (1964), 1–114. E. J. Beggs, The de Rham complex on infinite dimensional manifolds, Quart. J. Math. Oxford (2), 38 (1987), 131–154. D. Beltiţă, Asymptotic products and enlargibility of Banach–Lie algebras, J. Lie Theory, 14 (2004), 215–226. D. Beltiţă, Smooth Homogeneous Structures in Operator Theory, Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math., 2006. D. Beltiţă and K.-H. Neeb, Finite-dimensional Lie subalgebras of algebras with continuous inversion, preprint, 2006. D. Beltiţă and T. S. Ratiu, Geometric representation theory for unitary groups of operator algebras, Adv. Math., to appear. D. Beltiţă and T. S. Ratiu, Symplectic leaves in real Banach Lie–Poisson spaces, Geom. Funct. Anal., 15 (2005), 753–779. W. Bertram and K.-H. Neeb, Projective completions of Jordan pairs, Part I. The generalized projective geometry of a Lie algebra, J. Algebra, 277 (2004), 474–519. W. Bertram and K.-H. Neeb, Projective completions of Jordan pairs, Part II, Geom. Dedicata, 112 (2005), 75–115. W. Bertram, H. Glöckner and K.-H. Neeb, Differential Calculus over General Base Fields and Rings, Expo. Math., 22 (2004), 213–282. Y. Billig, Abelian extensions of the group of diffeomorphisms of a torus, Lett. Math. Phys., 64 (2003), 155–169. Y. Billig and A. Pianzola, Free Kac-Moody groups and their Lie algebras, Algebr. Represent. Theory, 5 (2002), 115–136. G. Birkhoff, Continuous groups and linear spaces, Mat. Sb., 1 (1936), 635–642. G. Birkhoff, Analytic groups, Trans. Amer. Math. Soc., 43 (1938), 61–101. B. Blackadar, K-theory for Operator Algebras, 2nd edition, Cambridge Univ. Press, 1998. J. Bochnak and J. Siciak, Analytic functions in topological vector spaces, Studia Math., 39 (1971), 77–112. S. Bochner and D. Montgomery, Groups of differentiable and real or complex analytic transformations, Ann. of Math. (2), 46 (1945), 685–694. F. F. Bonsall and J. Duncan, Complete Normed Algebras, Ergeb. Math. Grenzgeb., 80, Springer-Verlag, 1973. H. Boseck, G. Czichowski and K.-P. Rudolph, Analysis on Topological Groups – General Lie Theory, Teubner, Leipzig, 1981. J.-B. Bost, Principe d’Oka, K-theorie et systèmes dynamiques non-commutatifs, Invent. Math., 101 (1990), 261–333. R. Bott, On the characteristic classes of groups of diffeomorphisms, Enseign. Math. (2), 23 (1977), 209–220. N. Bourbaki, Topological Vector Spaces, Chaps. 1–5, Springer-Verlag, 1987. N. Bourbaki, Lie Groups and Lie Algebras, Chapter 1–3, Springer-Verlag, 1989. G. E. Bredon, Topology and Geometry, Grad. Texts in Math., 139, Springer-Verlag, 1993. J.-L. Brylinski, Loop Spaces, Characteristic Classes and Geometric Quantization, Progr. Math., 107, Birkhäuser, 1993. J. I. Burgos Gil, The Regulators of Beilinson and Borel, CRM Monogr., 15, Amer. Math. Soc., 2002. E. Calabi, On the group of automorphisms of a symplectic manifold, In: Probl. Analysis. Sympos. in Honor of Salomon Bochner, Princeton Univ. Press, Princeton, N.J., 1970, pp. 1–26. J. E. Campbell, On a law of combination of operators bearing on the theory of continuous transformation groups, Proc. London Math. Soc., 28 (1897), 381–390. J. E. Campbell, On a law of combination of operators. (second paper), Proc. London Math. Soc., 28 (1897), 381–390. E. Cartan, Les groupes bilinéaires et les systèmes de nombres complexes, Ann. Fac. Sci. Toulouse Sci. Math. Sci. Phys., 12 (1898), B1–B64. E. Cartan, L’intégration des systèmes d’équations aux diffrentielles totales, Ann. Sci. École Norm. Sup. (3), 18 (1901), 241–311. E. Cartan, Sur la structure des groups infinies des transformations, Ann. Sci. École. Norm. Sup., 21 (1904), 153–206; 22 (1905), 219–308. E. Cartan, Le troisième théorème fondamental de Lie, C. R. Math. Acad. Sci. Paris, 190 (1930), 914–916, 1005–1007. E. Cartan, La topologie des groupes de Lie. (Exposés de géométrie Nr. 8.), Actualités. Sci. Indust., 358 (1936), p. 28. E. Cartan, La topologie des espaces représentifs de groupes de Lie, Oeuvres I, Gauthier–Villars, Paris, 2 (1952), 1307–1330. G. Cassinelli, E. de Vito, P. Lahti and A. Levrero, Symmetries of the quantum state space and group representations, Rev. Math. Phys., 10 (1998), 893–924. P. Chernoff and J. Marsden, On continuity and smoothness of group actions, Bull. Amer. Math. Soc., 76 (1970), 1044–1049. C. Chevalley, Theory of Lie Groups I, Princeton Univ. Press, 1946. C. Chevalley and S. Eilenberg, Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc., 63 (1948), 85–124. A. Connes, Non-commutative Geometry, Academic Press, 1994. J. A. Cuenca Mira, A. Garcia Martin and C. Martin Gonzalez, Structure theory of L *-algebras, Math. Proc. Cambridge Philos. Soc., 107 (1990), 361–365. J. Dai and D. Pickrell, The orbit method and the Virasoro extension of ( \(\hbox{Diff}_+{\user2{\mathbb{S}}}^{1}\)). I. Orbital integrals, J. Geom. Phys., 44 (2003), 623–653. P. Dazord, Lie groups and algebras in infinite dimension: a new approach, In: Symplectic Geometry and Quantization, Contemp. Math., 179, Amer. Math. Soc., Providence, RI, 1994, pp. 17–44. J. Delsartes, Les groups de transformations linéaires dans l’espace de Hilbert, Mém. Sci. Math., 57, Paris. I. Dimitrov and I. Penkov, Weight modules of direct limit Lie algebras, Internat. Math. Res. Notices, 5 (1999), 223–249. P. Donato and P. Iglesias, Examples de groupes difféologiques: flots irrationnels sur le tore, C. R. Acad. Sci. Paris Ser. I Math., 301 (1985), 127–130. A. Douady and M. Lazard, Espaces fibrés en algèbres de Lie et en groupes, Invent. Math., 1 (1966), 133–151. A. Dress, Newman’s Theorem on transformation groups, Topology, 8 (1969), 203–207. E. B. Dynkin, Calculation of the coefficients in the Campbell–Hausdorff formula (Russian), Dokl. Akad. Nauk. SSSR (N.S.), 57 (1947), 323–326. E. B. Dynkin, Normed Lie Algebras and Analytic Groups, Amer. Math. Soc. Transl., 97 (1953), p. 66. D. G. Ebin, The manifold of Riemannian metrics, In: Global Analysis, Berkeley, Calif., 1968, Proc. Sympos. Pure Math., 15 (1970), pp. 11–40. D. G. Ebin and J. E. Marsden, Groups of diffeomorphisms and the solution of the classical Euler equations for a perfect fluid, Bull. Amer. Math. Soc., 75 (1969), 962–967. D. G. Ebin and J. E. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math., 92 (1970), 102–163. D. G. Ebin and G. Misiolek, The exponential map on \({\user1{\mathcal{D}}}^{s}_{\mu }\). In: The Arnoldfest, Toronto, ON, 1997, Fields Inst. Commun., 24, Amer. Math. Soc., Providence, RI, 1999, 153–163. J. Eells, Jr., On the geometry of function spaces, In: International Symposium on Algebraic Topology, Universidad Nacional Autonoma de México and UNESCO, Mexico City, pp. 303–308. J. Eells, Jr., A setting for global analysis, Bull. Amer. Math. Soc., 72 (1966), 751–807. J. Eichhorn and R. Schmid, Form preserving diffeomorphisms on open manifolds, Ann. Global Anal. Geom., 14 (1996), 147–176. J. Eichhorn and R. Schmid, Lie groups of Fourier integral operators on open manifolds, Comm. Anal. Geom., 9 (2001), 983–1040. M. Eichler, A new proof of the Baker–Campbell–Hausdorff formula, J. Math. Soc. Japan, 20 (1968), 23–25. W. T. van Est, Local and global groups, Proc. Konink. Nederl. Akad. Wetensch. Ser. A, 65; Indag. Math., 24 (1962), 391–425. W. T. van Est, On Ado’s theorem, Proc. Konink. Nederl. Akad. Wetensch. Ser. A, 69; Indag. Math., 28 (1966), 176–191. W. T. van Est, Rapport sur les S-atlas, Astérisque, 116 (1984), 235–292. W. T. van Est, Une démonstration de É. Cartan du troisième théorème de Lie, In: Seminaire Sud-Rhodanien de Geometrie VIII: Actions Hamiltoniennes de Groupes; Troisième Théorème de Lie, (eds. P. Dazord et al.), Hermann, Paris, 1988. W. T. van Est and Th. J. Korthagen, Non enlargible Lie algebras, Proc. Konink. Nederl. Akad. Wetensch. Ser. A; Indag. Math., 26 (1964), 15–31. W. T. van Est and S. Świerczkowski, The path functor and faithful representability of Banach Lie algebras, In: Collection of articles dedicated to the memory of Hannare Neumann, I., J. Austral. Math. Soc., 16 (1973), 54–69. P. I. Etinghof and I. B. Frenkel, Central extensions of current groups in two dimensions, Comm. Math. Phys., 165 (1994), 429–444. R. P. Filipkiewicz, Isomorphisms between diffeomorphism groups, Ergodic Theory Dynam. Systems, 2 (1983), 159–171. K. Floret, Lokalkonvexe Sequenzen mit kompakten Abbildungen, J. Reine Angew. Math., 247 (1971), 155–195. Ch. Freifeld, One-parameter subgroups do not fill a neighborhood of the identity in an infinite-dimensional Lie (pseudo-) group, Battelle Rencontres, 1967, Lectures Math. Phys., Benjamin, New York, 1968, 538–543. A. Frölicher and W. Bucher, Calculus in Vector Spaces without Norm, Lecture Notes in Math., 30, Springer-Verlag, 1966. A. Frölicher and A. Kriegl, Linear Spaces and Differentiation Theory, J. Wiley, Interscience, 1988. D. B. Fuks, Cohomology of Infinite-Dimensional Lie Algebras, Consultants Bureau, New York, London, 1986. G. Galanis, Projective limits of Banach–Lie groups, Period. Math. Hungar., 32 (1996), 179–191. G. Galanis, On a type of linear differential equations in Fréchet spaces, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 24 (1997), 501–510. S. L. Glashow, and M. Gell-Mann, Gauge theories of vector particles, Ann. Physics, 15 (1961), 437–460. H. Glöckner, Infinite-dimensional Lie groups without completeness restrictions, In: Geometry and Analysis on Finite and Infinite-dimensional Lie Groups, (eds. A. Strasburger, W. Wojtynski, J. Hilgert and K.-H. Neeb), Banach Center Publ., 55 (2002), 43–59. H. Glöckner, Algebras whose groups of units are Lie groups, Studia Math., 153 (2002), 147–177. H. Glöckner, Lie group structures on quotient groups and universal complexifications for infinite-dimensional Lie groups, J. Funct. Anal., 194 (2002), 347–409. H. Glöckner, Patched locally convex spaces, almost local mappings, and diffeomorphism groups of non-compact manifolds, TU Darmstadt, manuscript, 26.6.02. H. Glöckner, Implicit functions from topological vector spaces to Banach spaces, Israel J. Math., to appear, math.GM/0303320. H. Glöckner, Direct limit Lie groups and manifolds, J. Math. Kyoto Univ., 43 (2003), 1–26. H. Glöckner, Lie groups of measurable mappings, Canad. J. Math., 55 (2003), 969–999. H. Glöckner, Tensor products in the category of topological vector spaces are not associative, Comment. Math. Univ. Carolin., 45 (2004), 607–614. H. Glöckner, Lie groups of germs of analytic mappings, In: Infinite Dimensional Groups and Manifolds, (eds. V. Turaev and T. Wurzbacher), IRMA Lect. Math. Theor. Phys., de Gruyter, 2004, pp. 1–16. H. Glöckner, Fundamentals of direct limit Lie theory, Compositio Math., 141 (2005), 1551–1577. H. Glöckner, Discontinuous non-linear mappings on locally convex direct limits, Publ. Math. Debrecen, 68 (2006) 1–13. H. Glöckner, Fundamental problems in the theory of infinite-dimensional Lie groups, J. Geom. Symmetry Phys., 5 (2006), 24–35. H. Glöckner, Direct limits of infinite-dimensional Lie groups compared to direct limits in related categories, in preparation. H. Glöckner, Direct limit groups do not have small subgroups, preprint, math.GR/0602407. H. Glöckner and K.-H. Neeb, Banach–Lie quotients, enlargibility, and universal complexifications, J. Reine Angew. Math., 560 (2003), 1–28. H. Glöckner and K.-H. Neeb, Infinite-dimensional Lie groups, Vol. I, Basic Theory and Main Examples, book in preparation. H. Glöckner and K.-H. Neeb, Infinite-dimensional Lie groups, Vol. II, Geometry and Topology, book in preparation. G. A. Goldin, Lectures on diffeomorphism groups in quantum physics, In: Contemporary Problems in Mathematical Physics, Cotonue, 2003, Proc. of the third internat. workshop, 2004, pp. 3–93. R. Goodman and N. R. Wallach, Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle, J. Reine Angew. Math., 347 (1984), 69–133. R. Goodman and N. R. Wallach, Projective unitary positive energy representations of Diff \({\user2{\mathbb{S}}}^{1}\), J. Funct. Anal., 63 (1985), 299–312. M. Goto, On an arcwise connected subgroup of a Lie group, Proc. Amer. Math. Soc., 20 (1969), 157–162. J. Grabowski Free subgroups of diffeomorphism groups, Fund. Math., 131 (1988), 103–121. J. Grabowski, Derivative of the exponential mapping for infinite-dimensional Lie groups, Ann. Global Anal. Geom., 11 (1993), 213–220. J. M. Gracia-Bondia, J. C. Vasilly and H. Figueroa, Elements of Non-commutative Geometry, Birkhäuser Advanced Texts, Birkhäuser, Basel, 2001. B. Gramsch, Relative Inversion in der Störungstheorie von Operatoren und Ψ-Algebren, Math. Ann., 269 (1984), 22–71. H. Grundling and K.- H. Neeb, Lie group extensions associated to modules of continuous inverse algebras, in preparation. J. Gutknecht, Die C ∞ Γ-Struktur auf der Diffeomorphismengruppe einer kompakten Mannigfaltigkeit, Ph. D. thesis, Eidgenössische Technische Hochschule Zürich, Diss. No. 5879, Juris Druck + Verlag, Zurich, 1977. R. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc., 7 (1982), 65–222. P. de la Harpe, Classical Banach–Lie Algebras and Banach–Lie Groups of Operators in Hilbert Space, Lecture Notes in Math., 285, Springer-Verlag, 1972. L. A. Harris and W. Kaup, Linear algebraic groups in infinite dimensions, Illinois J. Math., 21 (1977), 666–674. F. Hausdorff, Die symbolische Exponentialformel in der Gruppentheorie, Leipziger Berichte, 58 (1906), 19–48. M. Hausner and J. T. Schwartz, Lie Groups; Lie Algebras, Gordon and Breach, New York, London, Paris, 1968. G. Hector and E. Macías-Virgós, Diffeological groups, Res. Exp. Math., 25 (2002), 247–260. A. Ya. Helemskii, Banach and Locally Convex Algebras, Oxford Sci. Publications, Oxford University Press, New York, 1993. S. Hiltunen, Implicit functions from locally convex spaces to Banach spaces, Studia Math., 134 (1999), 235–250. G. Hochschild, Group extensions of Lie groups I, II, Ann. of Math., 54 (1951), 96–109; 54 (1951), 537–551. G. Hochschild, The Structure of Lie Groups, Holden Day, San Francisco, 1965. K. H. Hofmann, Introduction to the Theory of Compact Groups. Part I, Dept. Math. Tulane Univ., New Orleans, LA, 1968. K. H. Hofmann, Die Formel von Campbell, Hausdorff und Dynkin und die Definition Liescher Gruppen, In: Theory Sets Topology in Honour of Felix Hausdorff, 1868–1942, VEB Deutsch, Verlag Wissensch., Berlin, 1972, pp. 251–264. K. H. Hofmann, Analytic groups without analysis, Sympos. Math., 16, Convegno sui Gruppi Topologici e Gruppi di Lie, INDAM, Rome, 1974, Academic Press, London, 1975, pp. 357–374. K. H. Hofmann and S. A. Morris, The Structure of Compact Groups, de Gruyter Stud. Math., de Gruyter, Berlin, 1998. K. H. Hofmann and S. A. Morris, Sophus Lie’s third fundamental theorem and the adjoint functor theorem, J. Group Theory, 8 (2005), 115–123. K. H. Hofmann and S. A. Morris, The Lie Theory of Connected Pro-Lie Groups–A Structure Theory for Pro-Lie Algebras, Pro-Lie Groups and Connected Locally Compact Groups, EMS Publishing House, Zürich, to appear (2006). K. H. Hofmann, S. A. Morris and D. Poguntke, The exponential function of locally connected compact abelian groups, Forum Math., 16 (2004), 1–16. K. H. Hofmann and K.-H. Neeb, Pro-Lie groups which are infinite-dimensional Lie groups, submitted. H. Hopf, Fundamentalgruppe und zweite Bettische Gruppe, Comment. Math. Helv., 14 (1942), 257–309. L. van Hove, Topologie des espaces fonctionnels analytiques, et des groups infinis des transformations, Acad. Roy. Belgique, Bull. Cl. Sci. (5), 38 (1952), 333–351. L. van Hove, L’ensemble des fonctions analytiques sur un compact en tant qu’algèbre topologique, Bull. Soc. Math. Belg., 1952, 8–17 (1953). R. S. Ismagilov, Representations of Infinite-Dimensional Groups, Transl. Math. Monogr., 152 (1996). V. G. Kac, Constructing groups associated to infinite-dimensional Lie algebras, In: Infinite-Dimensional Groups with Applications, (ed. V. Kac), MSRI Publications, 4, Springer-Verlag, 1985. V. G. Kac, Infinite-dimensional Lie Algebras, Cambridge University Press, 1990. V. G. Kac and D. H. Peterson, Regular functions on certain infinite-dimensional groups, In: Arithmetic and Geometry, (eds. M. Artin and J. Tate), 2, Birkhäuser, Boston, 1983. N. Kamran and T. Robart, A manifold structure for analytic Lie pseudogroups of infinite type, J. Lie Theory, 11 (2001), 57–80. N. Kamran and T. Robart, An infinite-dimensional manifold structure for analytic Lie pseudogroups of infinite type, Internat. Math. Res. Notices, 34 (2004), 1761–1783. W. Kaup, Über die Klassifikation der symmetrischen hermiteschen Mannigfaltigkeiten unendlicher Dimension I, Math. Ann., 257 (1981), 463–486. W. Kaup, A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces, Math. Z., 183 (1983), 503–529. W. Kaup, Über die Klassifikation der symmetrischen hermiteschen Mannigfaltigkeiten unendlicher Dimension II, Math. Ann., 262 (1983), 57–75. J. Kedra, D. Kotchick and S. Morita, Crossed flux homomorphisms and vanishing theorems for flux groups, preprint, Aug. 2005, math.AT/0503230. H. H. Keller, Differential Calculus in Locally Convex Spaces, Springer-Verlag, 1974. A. Kirillov, The orbit method beyond Lie groups. Infinite-dimensional groups, Surveys in modern mathematics, 292–304; London Math. Soc. Lecture Note Ser., 321, Cambridge Univ. Press, Cambridge, 2005. A. A. Kirillov and D. V. Yuriev, Kähler geometry of the infinite-dimensional homogeneous space \(M = \hbox{Diff}_+({\user2{\mathbb{S}}}^{1})/\hbox{Rot}({\user2{\mathbb{S}}}^{1})\), Funct. Anal. Appl., 21 (1987), 284–294. O. Kobayashi, A. Yoshioka, Y. Maeda and H. Omori, The theory of infinite-dimensional Lie groups and its applications, Acta Appl. Math., 3 (1985), 71–106. N. Kopell, Commuting diffeomorphisms, Proc. Sympos. Pure Math., 14 (1970), 165–184. B. Kostant, Quantization and unitary representations, In: Lectures in Modern Analysis and Applications III, Lecture Notes in Math., 170, Springer-Verlag, 1970, pp. 87–208. G. Köthe, Topological Vector Spaces I, Grundlehren der Math. Wissenschaften, 159, Springer-Verlag, Berlin etc., 1969. A. Kriegl and P. Michor, The Convenient Setting of Global Analysis, Math. Surveys Monogr., 53 (1997). A. Kriegl and P. Michor, Regular infinite-dimensional Lie groups, J. Lie Theory, 7 (1997), 61–99. N. H. Kuiper, The homotopy type of the unitary group of Hilbert space, Topology, 3 (1965), 19–30. S. Kumar, Kac-Moody Groups, their Flag Varieties and Representation Theory, Progr. Math., 204, Birkhäuser, Boston, MA, 2002. M. Kuranishi, On the local theory of continuous infinite pseudo groups I, Nagoya Math. J., 15 (1959), 225–260. F. Lalonde, D. McDuff and L. Polterovich, On the flux conjectures, In: Geometry, topology, and dynamics, Montreal, PQ, 1995, CRM Proc. Lecture Notes, 15, Amer. Math. Soc., Providence, RI, 1998, pp. 69–85. S. Lang, Fundamentals of Differential Geometry, Grad. Texts in Math., 191, Springer-Verlag, 1999. V. T. Laredo, Integration of unitary representations of infinite dimensional Lie groups, J. Funct. Anal., 161 (1999), 478–508. R. K. Lashof, Lie algebras of locally compact groups, Pacific J. Math., 7 (1957), 1145–1162. D. Laugwitz, Über unendliche kontinuierliche Gruppen. I. Grundlagen der Theorie; Untergruppen, Math. Ann., 130 (1955), 337–350. D. Laugwitz, Über unendliche kontinuierliche Gruppen. II. Strukturtheorie lokal Banachscher Gruppen, Bayer. Akad. Wiss. Math. Natur. Kl. Sitzungsber., 1956, 261–286 (1957). M. Lazard and J. Tits, Domaines d’injectivité de l’application exponentielle, Topology, 4 (1966), 315–322. P. Lecomte, Sur l’algèbre de Lie des sections d’un fibré en algèbre de Lie, Ann. Inst. Fourier, 30 (1980), 35–50. P. Lecomte, Sur la suite exacte canonique associée à un fibré principal, Bull. Soc. Math. France, 13 (1985), 259–271. L. Lempert, The Virasoro group as a complex manifold, Math. Res. Lett., 2 (1995), 479–495. L. Lempert, The problem of complexifying a Lie group, In: Multidimensional Complex Analysis and Partial Differential Equations, (eds. P. D. Cordaro et al.), Amer. Math. Soc., Contemp. Math., 205 (1997), 169–176. J. A. Leslie, On a theorem of E. Cartan, Ann. Mat. Pura Appl. (4), 74 (1966), 173–177. J. A. Leslie, On a differential structure for the group of diffeomorphisms, Topology, 6 (1967), 263–271. J. A. Leslie, Some Frobenius theorems in global analysis, J. Differential Geom., 2 (1968), 279–297. J. A. Leslie, On the group of real analytic diffeomorphisms of a compact real analytic manifold, Trans. Amer. Math. Soc., 274 (1982), 651–669. J. A. Leslie, A Lie group structure for the group of analytic diffeomorphisms, Boll. Un. Mat. Ital. A (6), 2 (1983), 29–37. J. A. Leslie, A path functor for Kac-Moody Lie algebras, In: Lie Theory, Differential Equations and Representation Theory, Montreal, PQ, 1989, Univ. Montreal, Montreal, QC, 1990, pp. 265–270. J. A. Leslie, Some integrable subalgebras of infinite-dimensional Lie groups, Trans. Amer. Math. Soc., 333 (1992), 423–443. J. A. Leslie, On the integrability of some infinite dimensional Lie algebras, Howard University, preprint, 1993. J. A. Leslie, On a diffeological group realization of certain generalized symmetrizable Kac-Moody Lie algebras, J. Lie Theory, 13 (2003), 427–442. D. Lewis, Formal power series transformations, Duke Math. J., 5 (1939), 794–805. S. Lie, Theorie der Transformationsgruppen I, Math. Ann., 16 (1880), 441–528. S. Lie, Unendliche kontinuierliche Gruppen, Abh. Sächs. Ges. Wiss., 21 (1895), 43–150. J.-L. Loday, Cyclic Homology, Grundlehren Math. Wiss., 301, Springer-Verlag, Berlin, 1998. O. Loos, Symmetric Spaces I: General Theory, Benjamin, New York, Amsterdam, 1969. M. V. Losik, Fréchet manifolds as diffeologic spaces, Russian Math., 36 (1992), 31–37. D. Luminet and A. Valette, Faithful uniformly continuous representations of Lie groups, J. London Math. Soc. (2), 49 (1994), 100–108. S. MacLane, Homology, Grundlehren Math. Wiss., 114, Springer-Verlag, 1963. S. MacLane, Origins of the cohomology of groups, Enseig. Math., 24 (1978), 1–29. Y. Maeda, H. Omori, O. Kobayashi and A. Yoshioka, On regular Fréchet-Lie groups. VIII. Primordial operators and Fourier integral operators, Tokyo J. Math., 8 (1985), 1–47. P. Maier, Central extensions of topological current algebras, In: Geometry and Analysis on Finite-and Infinite-Dimensional Lie Groups, (eds. A. Strasburger et al.), Banach Center Publ., 55, Warszawa, 2002. P. Maier and K.-H. Neeb, Central extensions of current groups, Math. Ann., 326 (2003), 367–415. B. Maissen, Lie-Gruppen mit Banachräumen als Parameterräume, Acta Math., 108 (1962), 229–269. B. Maissen, Über Topologien im Endomorphismenraum eines topologischen Vektorraums, Math. Ann., 151 (1963), 283–285. J. Marion and T. Robart, Regular Fréchet Lie groups of invertibe elements in some inverse limits of unital involutive Banach algebras, Georgian Math. J., 2 (1995), 425–444. J. E. Marsden, Hamiltonian one parameter groups: A mathematical exposition of infinite dimensional Hamiltonian systems with applications in classical and quantum mechanics, Arch. Rational Mech. Anal., 28 (1968), 362–396. J. E. Marsden and R. Abraham, Hamiltonian mechanics on Lie groups and Hydrodynamics, In: Global Analysis, (eds. S. S. Chern and S. Smale), Proc. Sympos. Pure Math., 16, 1970, Amer. Math. Soc., Providence, RI, pp. 237–244. L. Maurer, Über allgemeinere Invarianten-Systeme, Münchner Berichte, 43 (1888), 103–150. W. Mayer and T. Y. Thomas, Foundations of the theory of Lie groups, Ann. of Math., 36 (1935), 770–822. D. McDuff, Enlarging the Hamiltonian group, preprint, May 2005, math.SG/0503268. D. McDuff and D. Salamon, Introduction to Symplectic Topology, Oxford Math. Monogr., 1998. E. Michael, Convex structures and continuous selections, Canad. J. Math., 11 (1959), 556–575. A. D. Michal, Differential calculus in linear topological spaces, Proc. Nat. Acad. Sci. U. S. A., 24 (1938), 340–342. A. D. Michal, Differential of functions with arguments and values in topological abelian groups, Proc. Nat. Acad. Sci. U. S. A., 26 (1940), 356–359. A. D. Michal, The total differential equation for the exponential function in non-commutative normed linear rings, Proc. Nat. Acad. Sci. U. S. A., 31 (1945), 315–317. A. D. Michal, Differentiable infinite continuous groups in abstract spaces, Rev. Ci., Lima 50 (1948), 131–140. A. D. Michal and V. Elconin, Differential properties of abstract transformation groups with abstract parameters, Amer. J. Math., 59 (1937), 129–143. P. W. Michor, Manifolds of Differentiable Mappings, Shiva Publishing, Orpington, Kent (U.K.), 1980. P. W. Michor, A convenient setting for differential geometry and global analysis I, II, Cahiers. Topologie Géom. Différentielle Catég., 25 (1984), 63–109, 113–178. P. W. Michor, The cohomology of the diffeomorphism group of a manifold is a Gelfand-Fuks cohomology, In: Proc. of the 14th Winter School on Abstr. Analysis, Srni, 1986, Rend. Circ. Mat. Palermo (2) Suppl., 14, 1987, pp. 235–246. P. W. Michor, Gauge Theory for Fiber Bundles, Bibliopolis, ed. di fil. sci., Napoli, 1991. P. Michor and J. Teichmann, Description of infinite dimensional abelian regular Lie groups, J. Lie Theory, 9 (1999), 487–489. J. Mickelsson, Kac-Moody groups, topology of the Dirac determinant bundle, and fermionization, Comm. Math. Phys., 110 (1987), 173–183. J. Mickelsson, Current algebras and groups, Plenum Press, New York, 1989. J. Milnor, On infinite-dimensional Lie groups, Institute of Adv. Stud. Princeton, preprint, 1982. J. Milnor, Remarks on infinite-dimensional Lie groups, In: Relativité, groupes et topologie II, (eds. B. DeWitt and R. Stora), Les Houches, 1983, North Holland, Amsterdam, 1984, pp. 1007–1057. D. Montgomery and L. Zippin, Topological Transformation Groups, Interscience, New York, 1955. J. Moser, A new technique for the construction of solutions of nonlinear differential equations, Proc. Nat. Acad. Sci. U. S. A., 47 (1961), 1824–1831. S. B. Myers, Algebras of differentiable functions, Proc. Amer. Math. Soc., 5 (1954), 917–922. T. Nagano, Linear differential systems with singularities and an application to transitive Lie algebras, J. Math. Soc. Japan, 18 (1966), 398–404. M. Nagumo, Einige analytische Untersuchungen in linearen metrischen Ringen, Japan. J. Math., 13 (1936), 61–80. L. Natarajan, E. Rodriguez-Carrington and J. A. Wolf, Differentiable structure for direct limit groups, Lett. Math. Phys., 23 (1991), 99–109. L. Natarajan, E. Rodriguez-Carrington and J. A. Wolf, Locally convex Lie groups, Nova J. Algebra Geom., 2 (1993), 59–87. L. Natarajan, E. Rodriguez-Carrington and J. A. Wolf, New classes of infinite dimensional Lie groups, Proc. Sympos. Pure Math., 56 (1994), 377–392. L. Natarajan, E. Rodriguez-Carrington and J. A. Wolf, The Bott–Borel–Weil theorem for direct limit groups, Trans. Amer. Math. Soc., 353 (2001), 4583–4622. D. S. Nathan, One-parameter groups of transformations in abstract vector spaces, Duke Math. J., 1 (1935), 518–526. K.-H. Neeb, Holomorphic highest weight representations of infinite dimensional complex classical groups, J. Reine Angew. Math., 497 (1998), 171–222. K.-H. Neeb, Holomorphy and Convexity in Lie Theory, Expositions in Mathematics, 28, de Gruyter Verlag, Berlin, 1999. K.-H. Neeb, Representations of infinite dimensional groups, In: Infinite Dimensional Kähler Manifolds, (eds. A. Huckleberry and T. Wurzbacher), DMV Sem., 31, Birkhäuser, 2001, pp. 131–178. K.-H. Neeb, Locally finite Lie algebras with unitary highest weight representations, Manuscripta Math., 104 (2001), 343–358. K.-H. Neeb, Central extensions of infinite-dimensional Lie groups, Ann. Inst. Fourier, 52 (2002), 1365–1442. K.-H. Neeb, Classical Hilbert–Lie groups, their extensions and their homotopy groups, In: Geometry and Analysis on Finite and Infinite-dimensional Lie Groups, (eds. A. Strasburger, W. Wojtynski, J. Hilgert and K.-H. Neeb), Banach Center Publ., 55, Warszawa, 2002, pp. 87–151. K.-H. Neeb, A Cartan–Hadamard Theorem for Banach–Finsler manifolds, Geom. Dedicata, 95 (2002), 115–156. K.-H. Neeb, Universal central extensions of Lie groups, Acta Appl. Math., 73 (2002), 175–219. K.-H. Neeb, Locally convex root graded Lie algebras, Trav. Math., 14 (2003), 25–120. K.-H. Neeb, Abelian extensions of infinite-dimensional Lie groups, Trav. Math., 15 (2004), 69–194. K.-H. Neeb, Infinite-dimensional Lie groups and their representations, In: Lie Theory: Lie Algebras and Representations, (eds. J. P. Anker and B. Ørsted), Progr. Math., 228, Birkhäuser, 2004, pp. 213–328. K.-H. Neeb, Current groups for non-compact manifolds and their central extensions, In: Infinite Dimensional Groups and Manifolds, (ed. T. Wurzbacher), IRMA Lect. Math. Theor. Phys., 5, de Gruyter Verlag, Berlin, 2004, pp. 109–183. K.-H. Neeb, Non-abelian extensions of infinite-dimensional Lie groups, Ann. Inst. Fourier, to appear. K.-H. Neeb, Lie algebra extensions and higher order cocycles, J. Geom. Symmetry Phys., 5 (2006), 48–74. K.-H. Neeb, Non-abelian extensions of topological Lie algebras, Comm. Algebra, 34 (2006), 991–1041. K.-H. Neeb, On the period group of a continuous inverse algebra, in preparation. K.-H. Neeb and N. Stumme, On the classification of locally finite split simple Lie algebras, J. Reine Angew. Math., 533 (2001), 25–53. K.-H. Neeb and C. Vizman, Flux homomorphisms and principal bundles over infinite-dimensional manifolds, Monatsh. Math., 139 (2003), 309–333. K.-H. Neeb and F. Wagemann, The second cohomology of current algebras of general Lie algebras, Canad. J. Math., to appear. K.-H. Neeb and F. Wagemann, Lie group structures on groups of maps on non-compact manifolds, in preparation. E. Neher, Generators and relations for 3-graded Lie algebras, J. Algebra, 155 (1993), 1–35. E. Neher, Lie algebras graded by 3-graded root systems and Jordan pairs covered by grids, Amer. J. Math., 118 (1996), 439–491. J. von Neumann, Über die analytischen Eigenschaften von Gruppen linearer Transformationen, Math. Z., 30 (1929), 3–42. P. J. Olver, Applications of Lie Groups to Differential Equations, second edition, Grad. Texts in Math., 107, Springer-Verlag, New York, 1993. H. Omori, On the group of diffeomorphisms on a compact manifold, In: Global Analysis, Proc. Sympos. Pure Math., 15, Berkeley, Calif., 1968, Amer. Math. Soc., Providence, R.I., 1970, pp. 167–183. H. Omori, Groups of iffeomorphisms and their subgroups, Trans. Amer. Math. Soc., 179 (1973), 85–122. H. Omori, Infinite Dimensional Lie Transformation Groups, Lecture Notes Math., 427, Springer-Verlag, Berlin-New York, 1974. H. Omori, On Banach–Lie groups acting on finite-dimensional manifolds, Tôhoku Math. J., 30 (1978), 223–250. H. Omori, A method of classifying expansive singularities, J. Differential. Geom., 15 (1980), 493–512. H. Omori, A remark on non-enlargible Lie algebras, J. Math. Soc. Japan, 33 (1981), 707–710. H. Omori, Infinite-Dimensional Lie Groups, Transl. Math. Monogr., 158, Amer. Math. Soc., 1997. H. Omori and P. de la Harpe, Opération de groupes de Lie banachiques sur les variétés différentielles de dimension finie, C. R. Acad. Sci. Paris Sér. A-B, 273 (1971), A395–A397. H. Omori and P. de la Harpe, About interactions between Banach–Lie groups and finite dimensional manifolds, J. Math. Kyoto Univ., 12 (1972), 543–570. H. Omori, Y. Maeda and A. Yoshioka, On regular Fréchet-Lie groups. I. Some differential geometrical expressions of Fourier integral operators on a Riemannian manifold, Tokyo J. Math., 3 (1980), 353–390. H. Omori, Y. Maeda and A. Yoshioka, On regular Fréchet-Lie groups. II. Composition rules of Fourier-integral operators on a Riemannian manifold, Tokyo J. Math., 4 (1981), 221–253. H. Omori, Y. Maeda, A. Yoshioka and O. Kobayashi, On regular Fréchet-Lie groups. III. A second cohomology class related to the Lie algebra of pseudodifferential operators of order one, Tokyo J. Math., 4 (1981), 255–277. H. Omori, Y. Maeda, A. Yoshioka and O. Kobayashi, On regular Fréchet-Lie groups IV. Definition and fundamental theorems, Tokyo J. Math., 5 (1982), 365–398. H. Omori, Y. Maeda, A. Yoshioka and O. Kobayashi, On regular Fréchet-Lie groups. V. Several basic properties, Tokyo J. Math., 6 (1983), 39–64. H. Omori, Y. Maeda, A. Yoshioka and O. Kobayashi, On regular Fréchet-Lie groups. VI. Infinite-dimensional Lie groups which appear in general relativity, Tokyo J. Math., 6 (1983), 217–246. K. Ono, Floer-Novikov cohomology and the flux conjecture, preprint, 2004. J. T. Ottesen, Infinite Dimensional Groups and Algebras in Quantum Physics, Springer-Verlag, Lecture Notes in Phys., m 27, 1995. R. S. Palais, A Global Formulation of the Lie Theory of Transformation Groups, Mem. Amer. Math. Soc., 22, Amer. Math. Soc., 1957. V. P. Palamodov, Homological methods in the theory of locally convex spaces, Russian Math. Surveys, 26 (1971), 1–64. J. Palis, On Morse-Smale dynamical systems, Topology, 8 (1968), 385–404. J. Palis, Vector fields generate few diffeomorphisms, Bull. Amer. Math. Soc., 80 (1974), 503–505. V. G. Pestov, Nonstandard hulls of Banach–Lie groups and algebras, Nova J. Algebra Geom., 1 (1992), 371–381. V. G. Pestov, Free Banach–Lie algebras, couniversal Banach–Lie groups, and more, Pacific J. Math., 157 (1993), 137–144. V. G. Pestov, Enlargible Banach–Lie algebras and free topological groups, Bull. Austral. Math. Soc., 48 (1993), 13–22. V. G. Pestov, Correction to “Free Banach–Lie algebras, couniversal Banach–Lie groups, and more”, Pacific J. Math., 171 (1995), 585–588. V. G. Pestov, Regular Lie groups and a theorem of Lie-Palais, J. Lie Theory, 5 (1995), 173–178. D. Pickrell, Invariant Measures for Unitary Groups Associated to Kac-Moody Lie Algebras, Mem. Amer. Math. Soc., 693, 2000. D. Pickrell, On the action of the group of diffeomorphisms of a surface on sections of the determinant line bundle, Pacific J. Math., 193 (2000), 177–199. D. Pisanelli, An extension of the exponential of a matrix and a counter example to the inversion theorem in a space H(K), Rend. Mat. (6), 9 (1976), 465–475. D. Pisanelli, An example of an infinite Lie group, Proc. Amer. Math. Soc., 62 (1977), 156–160. D. Pisanelli, The second Lie theorem in the group Gh(n, \({\user2{\mathbb{C}}}\)), In: Advances in Holomorphy, (ed. J. A. Barroso), North Holland Publ., 1979. L. Polterovich, The geometry of the group of symplectic diffeomorphisms, Lectures Math., ETH Zürich, Birkhäuser, 2001. L. Pontrjagin, Topological Groups, Princeton Math. Ser., 2, Princeton University Press, Princeton, 1939. A. Pressley and G. Segal, Loop Groups, Oxford University Press, Oxford, 1986. M. E. Pursell, Algebraic structures associated with smooth manifolds, Thesis, Purdue Univ., 1952. M. E. Pursell and M. E. Shanks, The Lie algebra of a smooth manifold, Proc. Amer. Math. Soc., 5 (1954), 468–472. C. R. Putnam and A. Winter, The orthogonal group in Hilbert space, Amer. J. Math., 74 (1952), 52–78. T. Ratiu and A. Odzijewicz, Banach Lie–Poisson spaces and reduction, Comm. Math. Phys., 243 (2003), 1–54. T. Ratiu and A. Odzijewicz, Extensions of Banach Lie–Poisson spaces, J. Funct. Anal., 217 (2004), 103–125. T. Ratiu and R. Schmid, The differentiable structure of three remarkable diffeomorphism groups, Math. Z., 177 (1981), 81–100. J. F. Ritt, Differential groups and formal Lie theory for an infinite number of parameters, Ann. of Math. (2), 52 (1950), 708–726. T. Robart, Groupes de Lie de dimension infinie. Second et troisième théorèmes de Lie. I. Groupes de première espèce, C. R. Acad. Sci. Paris Sér. I Math., 322 (1996), 1071–1074. T. Robart, Sur l’intégrabilité des sous-algèbres de Lie en dimension infinie, Canad. J. Math., 49 (1997), 820–839. T. Robart, Around the exponential mapping, In: Infinite Dimensional Lie Groups in Geometry and Representation Theory, World Sci. Publ., River Edge, NJ, 2002, pp. 11–30. T. Robart, On Milnor’s regularity and the path-functor for the class of infinite dimensional Lie algebras of CBH type, Algebras Groups Geom., 21 (2004), 367–386. T. Robart and N. Kamran, Sur la théorie locale des pseudogroupes de transformations continus infinis. I, Math. Ann., 308 (1997), 593–613. E. Rodriguez-Carrington, Lie groups associated to Kac–Moody Lie algebras: an analytic approach, In: Infinite-dimensional Lie Algebras and Groups, Luminy-Marseille, 1988, Adv. Ser. Math. Phys., 7, World Sci. Publ., Teaneck, NJ, 1989, pp. 57–69. C. Roger, Extensions centrales d’algèbres et de groupes de Lie de dimension infinie, algèbres de Virasoro et généralisations, Rep. Math. Phys., 35 (1995), 225–266. J. Rosenberg, Algebraic K-theory and its Applications, Grad. Texts in Math., 147, Springer-Verlag, 1994. W. Rudin, Functional Analysis, McGraw Hill, 1973. R. Schmid, Infinite-dimensional Hamiltonian Systems, Monographs and Textbooks in Physical Science, Lecture Notes, 3, Bibliopolis, Naples, 1987. R. Schmid, Infinite dimensional Lie groups with applications to mathematical physics, J. Geom. Symmetry Phys., 1 (2004), 54–120. R. Schmid, M. Adams and T. Ratiu, The group of Fourier integral operators as symmetry group, In: XIIIth International Colloquium on Group Theoretical Methods in Physics, College Park, Md., 1984, World Sci. Publ., Singapore, 1984, pp. 246–249. J. R. Schue, Hilbert space methods in the theory of Lie algebras, Trans. Amer. Math. Soc., 95 (1960), 69–80. J. R. Schue, Cartan decompositions for L *-algebras, Trans. Amer. Math. Soc., 98 (1961), 334–349. F. Schur, Neue Begründung der Theorie der endlichen Transformationsgruppen, Math. Ann., 35 (1890), 161–197. F. Schur, Beweis für die Darstellbarkeit der infinitesimalen Transformationen aller transitiven endlichen Gruppen durch Quotienten beständig convergenter Potenzreihen, Leipz. Ber., 42 (1890), 1–7. G. Segal, Unitary representations of some infinite-dimensional groups, Comm. Math. Phys., 80 (1981), 301–342. J.-P. Serre, Lie Algebras and Lie Groups, Lecture Notes in Math., 1500, Springer-Verlag, 1965 (1st ed.). I. M. Singer and S. Sternberg, The infinite groups of Lie and Cartan. I. The transitive groups, J. Anal. Math., 15 (1965), 1–114. J.-M. Souriau, Groupes différentiels de physique mathématique, In: Feuilletages et Quantification Géometrique, (eds. P. Dazord and N. Desolneux-Moulis), Journ. lyonnaises Soc. math. France, 1983, Sémin. sud-rhodanien de Géom. II, Hermann, Paris, 1984, pp. 73–119. J.-M. Souriau, Un algorithme générateur de structures quantiques, Soc. Math. Fr., Astérisque, hors série, 1985, 341–399. S. Sternberg, Infinite Lie groups and the formal aspects of dynamical systems, J. Math. Mech., 10 (1961), 451–474. N. Stumme, The Structure of Locally Finite Split Lie algebras, Ph. D. thesis, Darmstadt University of Technology, 1999. H. J. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc., 180 (1973), 171–188. K. Suto, Groups associated with unitary forms of Kac–Moody algebras, J. Math. Soc. Japan, 40 (1988), 85–104. K. Suto, Borel–Weil type theorem for the flag manifold of a generalized Kac–Moody algebra, J. Algebra, 193 (1997), 529–551. R. G. Swan, Vector bundles and projective modules, Trans. Amer. Math. Soc., 105 (1962), 264–277. S. Swierczkowski, Embedding theorems for local analytic groups, Acta Math., 114 (1965), 207–235. S. Swierczkowski, Cohomology of local group extensions, Trans. Amer. Math. Soc., 128 (1967), 291–320. S. Swierczkowski, The path-functor on Banach Lie algebras, Nederl. Akad. Wet., Proc. Ser. A, 74; Indag. Math., 33 (1971), 235–239. A. Tagnoli, La varietà analitiche reali come spazi omogenei, Boll. Un. Mat. Ital. (s4), 1 (1968), 422–426. J. Tits, Liesche Gruppen und Algebren, Springer-Verlag, 1983. F. Treves, Topological Vector Spaces, Distributions, and Kernels, Academic Press, New York, 1967. H. Upmeier, Symmetric Banach Manifolds and Jordan C *-algebras, North Holland Mathematics Studies, 1985. V. S. Varadarajan, Lie Groups, Lie Algebras, and Their Representations, Grad. Texts in Math., 102, Springer-Verlag, 1984. D. Vogt, On the functors Ext1 (E,F) for Fréchet spaces, Studia Math., 85 (1987), 163–197. L. Waelbroeck, Les algèbres à inverse continu, C. R. Acad. Sci. Paris, 238 (1954), 640–641. L. Waelbroeck, Le calcul symbolique dans les algèbres commutatives, J. Math. Pures Appl., 33 (1954), 147–186. L. Waelbroeck, Structure des algèbres à inverse continu, C. R. Acad. Sci. Paris, 238 (1954), 762–764. L. Waelbroeck, Topological Vector Spaces and Algebras, Springer-Verlag, 1971. G. Warner, Harmonic Analysis on Semisimple Lie Groups I, Springer-Verlag, 1972. A. Weinstein, Symplectic structures on Banach manifolds, Bull. Amer. Math. Soc., 75 (1969), 1040–1041. D. Werner, Funktionalanalysis, Springer-Verlag, 1995. H. Wielandt, Über die Unbeschränktheit der Operatoren der Quantenmechanik, Math. Ann., 121 (1949), p. 21. Chr. Wockel, The Topology of Gauge Groups, submitted, math-ph/0504076. Chr. Wockel, Smooth Extensions and Spaces of Smooth and Holomorphic Mappings, J. Geom. Symmetry Phys., 5 (2006), 118–126, math.DG/0511064. W. Wojtyński, Effective integration of Lie algebras, J. Lie Theory, 16 (2006), 601–620. J. A. Wolf, Principal series representations of direct limit groups, Compositio Math., 141 (2005), 1504–1530. M. Wüstner, Supplements on the theory of exponential Lie groups, J. Algebra, 265 (2003), 148–170. M. Wüstner, The classification of all simple Lie groups with surjective exponential map, J. Lie Theory, 15 (2005), 269–278. K. Yosida, On the groups embedded in the metrical complete ring, Japan. J. Math., 13 (1936), 7–26.