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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

Symplectic groupoids and Poisson manifolds

Author(s): Alan Weinstein
Journal: Bull. Amer. Math. Soc. 16 (1987), 101-104.
MSC (1985): Primary 58F05; Secondary 20L15
MathSciNet review: 866024
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References:

1.
R. Almeida and P. Molino, Suites d'Atiyah et feuilletages transversalement complets, C. R. Acad. Sci. Paris Sér. I 300 (1985), 13-15. MR 778785
2.
F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz and D. Sternheimer, Deformation theory and quantization. I, II, Ann. Phys. 111 (1977), 61-151. MR 496157
3.
A. Connes, A survey of foliations and operator algebras, Operator Algebras and Applications (R. V. Kadison, ed.), Proc. Sympos. Pure Math., vol. 38, Amer. Math. Soc. Providence, R.I., 1982, pp. 521-628. MR 679730
4.
A. Coste, D. Sondaz and A. Weinstein, Groupoĩdes sympléctiques et variétés de Poisson (notes d'un cours de A. Weinstein), Publications du Département de Mathématiques, Université Claude-Bernard Lyon I (en préparation, 1986).
5.
A. Douady and M. Lazard, Espaces fibrés en algèbres de Lie et en groupes, Invent. Math. 1 (1966), 133-151. MR 197622
6.
J. J. Duistermaat and H. J. Heekman, On the variation in the cohomology of the symplectic form of the reduced phase space, Invent. Math. 69 (1982), 259-268. MR 674406
7.
W. T. van Est, Rapport sur les S-atlas, Structure Transverse des Feuilletages, Astérisque 116 (1984), 235-292. MR 755174
8.
W. T. van Est and T. J. Korthagen, Non-enlargible Lie algebras, Indag. Math. 26 (1964), 15-31. MR 160851
9.
M. V. Karasev and V. P. Maslov, Operators with general commutation relations and their applications. I, Unitary-nonlinear operator equations, J. Soviet Math. 15 (1981), 273-368.
10.
M. V. Karasev and V. P. Maslov, Asymptotic and geometric quantization, Russian Math. Surveys 39:6 (1984), 133-205. MR 771100
11.
P. Libermann, Sur les groupoĩdes différentiates et le "presque parallelisme", Symposia Math. 10 (1972), 59-93. MR 370668
12.
M. Plaisant, Q-variétés banachiques. Application a l'integrabilité des algèbres de Lie, C. R. Acad. Sci. Paris 290A (1980), 185-188. MR 564157
13.
J. Pradines, Théorie de Lie pour les groupoĩdes différentiates. Calcul différentiel dans la catégorie des groupoĩdes infinitésimaux, C. R. Acad. Sci. Paris 264 (1967), 245-248. MR 216409
14.
J. Renault, A groupoid approach to C* algebras, Lecture Notes in Math., vol. 793, Springer-Verlag, Berlin and New York, 1980. MR 584266
15.
S. Sternberg, On minimal coupling and the symplectic mechanics of a classical particle in the presence of a Yang-Mills field, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), 5253-5254. MR 458486
16.
A. Weinstein, A universal phase space for particles in Yang-Mills fields, Lett. Math. Phys. 2 (1978), 417-420. MR 507025
17.
A. Weinstein, Symplectic geometry, Bull. Amer. Math. Soc. (N.S.) 5 (1981), 1-13. MR 614310
18.
A. Weinstein, The local structure of Poisson manifolds, J. Differential Geom. 18 (1983), 523-557. MR 723816
19.
H. E. Winkelnkemper, The graph of a foliation, Ann. Global Analysis and Geometry 1 (1983), 51-75. MR 739904
20.
M. V. Karasev, Quantization of nonlinear Lie-Poisson brackets in quasi-classical approximation, Preprint, Institute for Theoretical Physics, Kiev, 1985.

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Additional Information:

DOI: 10.1090/S0273-0979-1987-15473-5
PII: S 0273-0979(1987)15473-5


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