Conformal field theory and elliptic cohomology
Tài liệu tham khảo
Ando, 2000, Power operations in elliptic cohomology and representations of loop groups, Trans. Amer. Math. Soc., 352, 5619, 10.1090/S0002-9947-00-02412-0
Borcherds, 1992, Monstrous moonshine and monstrous Lie superalgebras, Invent. Math., 109, 405, 10.1007/BF01232032
F. Borceux, Handbook of categorical algebra 1–2, Encyclopedia of Mathematics and its Applications, Vols. 50–52, Cambridge University Press, Cambridge.
N. Bourbaki, Groups et algebres de Lie, Éléments de Mathématique, fascicule XXXIV, Hermann, Paris, 1968 (Chapitres 4,5 et 6).
Conway, 1979, Monstrous moonshine, Bull. AMS, 11, 308
Conway, 1999
Deligne, 1991, Le symbole modére, Inst. Hautes Études Sci. Publ. Math., 73, 147, 10.1007/BF02699258
Dong, 1993, Vertex algebras associated with even lattices, J. Algebra, 161, 245, 10.1006/jabr.1993.1217
Dong, 1998, Twisted representations of vertex operator algebras, Math. Ann., 310, 571, 10.1007/s002080050161
T. Fiore, Lax limits, lax adjoints and lax algebras, preprint, 2003.
I.B. Frenkel, Representation of Kac-Moody algebras and dual resonance model, in: M. Flato, et al. (Eds.), Applications of Group Theory in Theoretical Physics, Lectures in Applied Mathematics, Vol. 21, AMS, Providence, RI, 1985, pp. 325–353.
Frenkel, 2002, Vertex algebras and algebraic curves, Séminaire Bourbaki, Vol. 1999/2000, Astérisque, 276, 299
Frenkel, 1988
T. Gannon, C.S. Lam, Lattice and θ-function identities II: theta series, J. Math. Phys. 33 (1992), 3, 871–887.
Goddard, 1972, Compatibility of the dual Pomeron with unitarity and the absence of ghosts in the dual resonance model, Phys. Lett. B, 40, 235, 10.1016/0370-2693(72)90420-0
B.R. Greene, String theory on Calabi–Yau manifolds, preprint, hep-th/9702155.
Griess, 1982, The friendly giant, Invent. Math., 69, 1, 10.1007/BF01389186
M.J. Hopkins, M. Mahowald, The structure of 24 dimensional manifolds having normal bundles which lift to BO [8], Recent progress in homotopy theory (Baltimore, MD, 2000) Contemp. Math. 293, pp. 89–110.
M.J. Hopkins, H. Miller, in preparation.
P. Hu, I. Kriz, D-brane cohomology and elliptic cohomology, preprint, 2003.
Y.Z. Huang, A nonmeromorphic extension of the Moonshine module vertex operator algebra, Moonshine, the Monster, and Related Topics (South Hadley, MA, 1994) Contemporary Mathematics Vol. 193, Amer. Math. Soc., Providence, RI, 1996, pp. 123–148.
Huang, 1997
Huang, 1999, Intertwining operator algebras and vertex tensor categories for affine Lie algebras, Duke Math. J., 99, 113, 10.1215/S0012-7094-99-09905-2
Hurwitz, 1944
Jurisich, 1995, Realization of the Monster Lie algebra, Selecta Math. (N.S.), 1, 129, 10.1007/BF01614075
I. Kriz, On Spin and modularity in conformal field theory, Ann. Sci. de ENS 36 (4) (2003), 1, 57–112.
Lawvere, 1963, Functorial semantics of algebraic theories, Proc. Nat. Acad. Sci. USA, 50, 869, 10.1073/pnas.50.5.869
May, 1999
Moore, 1989, Classical and quantum conformal field theory, Comm. Math. Phys., 123, 177, 10.1007/BF01238857
Mumford, 1983
Mumford, 1991
S.P. Norton, More on Moonshine, Computational Group Theory, Academic Press, London, 1984, pp. 185–195.
Pressley, 1986
J. Rognes, Elliptic cohomology and algebraic K-theory of 2-vector spaces, preprint.
Sato, 1977, A classification of irreducible prehomogeneous vector spaces and their relative invariants, Nagoya Math. J., 65, 1, 10.1017/S0027763000017633
G. Segal, The definition of conformal field theory, preprint, cca. 1984.
G. Segal, Elliptic cohomology, Séminaire Bourbaki, Vol. 1987/88, Astérisque No. 161–162 1988; Exp. 695(4) (1989) 187–201.
Serre, 1973, 10.1007/978-1-4684-9884-4
V.P. Snaith, Algebraic cobordism and K-theory, Mem. Amer. Math. Soc. 21 (221) (l979) vii+152 pp.
Snaith, 1981, Localized stable homotopy of some classifying spaces, Math. Proc. Cambridge Philos. Soc., 89, 325, 10.1017/S0305004100058205
Thomas, 1999
M.P. Tuite, Generalized moonshine and abelian orbifold constructions, Moonshine, the Monster and Related Topics (South Hadley, MA, 1994) Contemporary Mathematics, Vol. 193, Amer. Math. Soc., Providence, RI, 1996, pp. 353–368.
Tuite, 1992, Monstrous moonshine from orbifolds, Comm. Math. Phys., 146, 277, 10.1007/BF02102629
Tuite, 1995, On the relationship between monstrous moonshine and the uniqueness of the moonshine module, Comm. Math. Phys., 166, 495, 10.1007/BF02099885
Verlinde, 1988, Fusion rules and modular transformations in 2D conformal field theory, Nucl. Phys. B, 300, 360, 10.1016/0550-3213(88)90603-7
Zamolodchikov, 1986, Disorder fields in two-dimensional conformal quantum-field theory and N=2 extended supersymmetry, Sov. Phys. JETP, 63, 913
Zhu, 1996, Modular invariance of characters of vertex operator algebras, J. Amer. Math. Soc., 9, 237, 10.1090/S0894-0347-96-00182-8