Lie bialgebroids and Poisson groupoids
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[1] R. Abraham and J. Marsden, <i>Foundations of Mechanics</i>, 2nd ed., Addison-Wesley, New York, 1985.
[2] C. Albert and P. Dazord, <i>Théorie des groupoïdes symplectiques. Chapitre II. Groupoïdes symplectiques</i>, Publications du Département de Mathématiques. Nouvelle série, Publ. Dép. Math. Nouvelle Sér., vol. 1990, Univ. Claude-Bernard, Lyon, 1990, pp. 27–99.
[3] A. L. Besse, <i>Manifolds All of Whose Geodesics Are Closed</i>, Ergeb. Math. Grenzgeb. (3), vol. 93, Springer-Verlag, Berlin, 1978.
[4] A. Coste, P. Dazord, and A. Weinstein, <i>Groupoïdes symplectiques</i>, Publications du Département de Mathématiques. Nouvelle Série. A, Vol. 2, Publ. Dép. Math. Nouvelle Sér. A, vol. 87, Univ. Claude-Bernard, Lyon, 1987, i–ii, 1–62.
[5] T. J. Courant, <i>Dirac manifolds</i>, Trans. Amer. Math. Soc. <b>319</b> (1990), no. 2, 631–661.
[7] V. G. Drinfel'd, <i>Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of classical Yang-Baxter equation</i>, Soviet Math. Dokl. <b>27</b> (1983), 68–71.
[8] V. G. Drinfel'd, <i>Quantum groups</i>, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), Amer. Math. Soc., Providence, RI, 1987, pp. 798–820.
[9] P. J. Higgins and K. C. H. Mackenzie, <i>Algebraic constructions in the category of Lie algebroids</i>, J. Algebra <b>129</b> (1990), no. 1, 194–230.
[10] P. J. Higgins and K. C. H. Mackenzie, <i>Duality for base-changing morphisms of vector bundles, modules, Lie algebroids and Poisson bundles</i>, to appear in Math. Proc. Cambridge Philos. Soc.
[11] M. V. Karasev, <i>Analogues of the objects of Lie group theory for nonlinear Poisson brackets</i>, Math. USSR-Izv. <b>28</b> (1987), 497–527.
[12] Y. Kosmann-Schwarzbach and F. Magri, <i>Poisson-Nijenhuis structures</i>, Ann. Inst. H. Poincaré Phys. Théor. <b>53</b> (1990), no. 1, 35–81.
[13] B. Kostant and S. Sternberg, <i>Anti-Poisson algebras and current algebras</i>, preprint.
[14] A. Lichnerowicz, <i>Les variétés de Poisson et leurs algèbres de Lie associées</i>, J. Differential Geometry <b>12</b> (1977), no. 2, 253–300.
[15] Jiang-Hua Lu and A. Weinstein, <i>Groupoïdes symplectiques doubles des groupes de Lie-Poisson</i>, C. R. Acad. Sci. Paris Sér. I Math. <b>309</b> (1989), no. 18, 951–954.
[16] Jiang-Hua Lu and A. Weinstein, <i>Poisson Lie groups, dressing transformations, and Bruhat decompositions</i>, J. Differential Geom. <b>31</b> (1990), no. 2, 501–526.
[17] K. C. H. Mackenzie, <i>Lie Groupoids and Lie Algebroids in Differential Geometry</i>, London Math. Soc. Lecture Note Ser., vol. 124, Cambridge University Press, Cambridge, 1987.
[18] K. C. H. Mackenzie, <i>Double Lie algebroids and second-order geometry. I</i>, Adv. Math. <b>94</b> (1992), no. 2, 180–239.
[19] S. Majid, <i>Matched pairs of Lie groups associated to solutions of the Yang-Baxter equations</i>, Pacific J. Math. <b>141</b> (1990), no. 2, 311–332.
[20] J. Pradines, <i>Fibrés vectoriels doubles et calculs des jets non holonomes</i>, Amiens, 1974, notes polycopiées.
[21] J. Pradines, <i>Remarque sur le groupoïde cotangent de Weinstein-Dazord</i>, C. R. Acad. Sci. Paris Sér. I Math. <b>306</b> (1988), no. 13, 557–560.
[22] N. Reshetikhin and M. A. Semenov-Tian-Shansky, <i>Quantum $R$-matrices and factorization problems</i>, J. Geom. Phys. <b>5</b> (1988), no. 4, 533–550 (1989).
[23] W. M. Tulczyjew, <i>A symplectic formulation of particle dynamics</i>, Differential Geometric Methods in Mathematical Physics (Proc. Sympos., Univ. Bonn, Bonn, 1975) eds. K. Bleuler and A. Reetz, Lecture Notes in Math., vol. 570, Springer-Verlag, Berlin, 1977, pp. 457–463.
[24] A. Weinstein, <i>Coisotropic calculus and Poisson groupoids</i>, J. Math. Soc. Japan <b>40</b> (1988), no. 4, 705–727.