Bulletin of the American Mathematical Society

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Book Information:

Author: N. V. Karasev and V. P. Maslov
Title: Nonlinear Poisson brackets, geometry and quantization
Additional book information: Translations of Math. Monographs, vol. 119, Amer. Math. Soc., Providence, RI, 1993, xi + 366 pp., ISBN 0-8218-4596-9, $170.00$

Claude Albert and Pierre Dazord, Groupoïdes de Lie et groupoïdes symplectiques, Symplectic geometry, groupoids, and integrable systems (Berkeley, CA, 1989) Math. Sci. Res. Inst. Publ., vol. 20, Springer, New York, 1991, pp. 1–11 (French). MR 1104916, DOI 10.1007/978-1-4613-9719-9_{1}

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Alain Connes, Géométrie non commutative, InterEditions, Paris, 1990 (French). MR 1079062

A. Coste, P. Dazord, and A. Weinstein, Groupoïdes symplectiques, Publications du Département de Mathématiques. Nouvelle Série. A, Vol. 2, Publ. Dép. Math. Nouvelle Sér. A, vol. 87, Univ. Claude-Bernard, Lyon, 1987, pp. i–ii, 1–62 (French). MR 996653

P. Dazord and G. Hector, Intégration symplectique des variétés de Poisson totalement asphériques, Symplectic geometry, groupoids, and integrable systems (Berkeley, CA, 1989) Math. Sci. Res. Inst. Publ., vol. 20, Springer, New York, 1991, pp. 37–72 (French, with English summary). MR 1104919, DOI 10.1007/978-1-4613-9719-9_{4}

P. Dazord and G. Patissier, La première classe de Chern comme obstruction à la quantification asymptotique, Symplectic geometry, groupoids, and integrable systems (Berkeley, CA, 1989) Math. Sci. Res. Inst. Publ., vol. 20, Springer, New York, 1991, pp. 73–97 (French). MR 1104920, DOI 10.1007/978-1-4613-9719-9_{5}

Marc De Wilde and Pierre B. A. Lecomte, Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds, Lett. Math. Phys. 7 (1983), no. 6, 487–496. MR 728644, DOI 10.1007/BF00402248

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André Lichnerowicz, Les variétés de Poisson et leurs algèbres de Lie associées, J. Differential Geometry 12 (1977), no. 2, 253–300 (French). MR 501133

J.-M. Souriau, Structure des systèmes dynamiques, Dunod, Paris, 1970 (French). Maîtrises de mathématiques. MR 0260238

Izu Vaisman, Lectures on the geometry of Poisson manifolds, Progress in Mathematics, vol. 118, Birkhäuser Verlag, Basel, 1994. MR 1269545, DOI 10.1007/978-3-0348-8495-2

Alan Weinstein, The local structure of Poisson manifolds, J. Differential Geom. 18 (1983), no. 3, 523–557. MR 723816

Alan Weinstein, Symplectic groupoids and Poisson manifolds, Bull. Amer. Math. Soc. (N.S.) 16 (1987), no. 1, 101–104. MR 866024, DOI 10.1090/S0273-0979-1987-15473-5

Alan Weinstein, Noncommutative geometry and geometric quantization, Symplectic geometry and mathematical physics (Aix-en-Provence, 1990) Progr. Math., vol. 99, Birkhäuser Boston, Boston, MA, 1991, pp. 446–461. MR 1156554

Alan Weinstein and Ping Xu, Extensions of symplectic groupoids and quantization, J. Reine Angew. Math. 417 (1991), 159–189. MR 1103911

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C. Albert, P. Dazord, Groupoïdes de Lie et groupoïdes symplectiques, Sém. sud-Rhodanien à Berkeley, Symplectic Geometry and Groupoids and Integrable Systems, M.S.R.I. Publications, no. 20, Springer-Verlag, Berlin and New York, 1991, pp. (1--11), MR 1104916.

[B.F.F.L.S]

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[C]

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[Co]

A. Connes, Géométrie non commutative, InterÉditions, Paris, 1990, MR 1079062.

[C.D.W]

A. Coste, P. Dazord, A. Weinstein, Groupoïdes symplectiques, Public. Dept. Math. Lyon (1987), 1--62, MR 0996653.

[D.H]

P. Dazord, G. Hector, Intégration symplectique des variétés de Poisson, Sém. sud-Rhodanien à Berkeley, Symplectic Geometry, Groupoids and Integrable Systems,
M.S.R.I. Publications, no. 20, Springer-Verlag, Berlin and New York, 1991, pp. (37--72), MR 1104919.

[D.P].

P. Dazord, G. Patissier, La première classe de Chern comme obstruction à la quantification asymptotique, Sém. sud-Rhodanien à Berkeley, Symplectic Geometry and Groupoids and Integable Systems, M.S.R.I. Publications, no. 20, Springer-Verlag,
Berlin and New York, 1991, pp. (73--97), MR 1104920.

[DW.L]

M. De Wilde, P. Lecomte, Existence of star-products and of formal deformation of the Poisson-Lie algebra of arbitrary symplectic manifolds, Letters in Math. Phys. 7 (1983), 487--496, MR 0728644.

[E]

C. Ehresmann, Colloque de topologie (espaces fibrés, Bruxelle, 1950), Thone, Liège, and Masson, Paris, 1951, pp. (29--55), MR 13:159.

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M. M. Karasev, Analogues of objects of Lie group theory for non linear Poisson brackets, Math. USSR Izvestiya, vol. 28, 1987, pp. (497--527), MR 0854594.

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A. Kirillov, Local Lie algebras, Russian Math. Surveys 31 (1976), 55--75 , MR 55:11304.

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B. Kostant, Quantization and unitary representations, Lecture Notes in Math., vol.
170, Springer-Verlag, Berlin-Heidelberg-New York, 1970, pp. (87--207), MR 0294568.

[Lb]

P. Libermann, Problèmes d'équivalence et géométrie symplectique, III Rencontres du Schnepfenried, Astérisque 107/108, vol. I, 1983, pp. (43--68), MR 0753129.

[L.M]

P. Libermann, C. Marle, Symplectic geometry and analytical mechanics, D. Reidel Publ. Comp., Dordrechet-Boston, 1987, MR 0882548.

[Lc]

A. Lichnerowicz, Les variétés de Poisson et leurs algèbres de Lie associées, J. Diff. Geometry 12 (1977), 253--300, MR 0501133.

[S]

J.-M. Souriau, Structure des systèmes dynamiques, Dunod, Paris, 1970, MR 0260238.

[V]

I. Vaisman, Lectures on the geometry of Poisson manifolds, Progress in Math., vol. 118, Birkhäuser, Basel-Boston-Berlin, 1994, MR 1269545.

[W1]

A. Weinstein, The local structure of Poisson manifolds, J. Diff. Geometry 18 (1983), 523--557 ; MR 87k:58099, MR 0723816.

[W2]

------, Symplectic groupoids and Poisson manifolds, Bull. Amer. Math. Soc. (N.S.) 16 (1987), 101--103, MR 0866024.

[W3]

------, Noncommutative geometry and geometric quantization, Symplectic Geometry and Mathematical Physics, Actes du Colloque J.-M. Souriau, Progress in Math., vol. 99, Birkhäuser, Basel-Boston-Berlin, 1991, pp. (462--476), MR 1156554.

[W.X]

A. Weinstein, P. Xu, Extensions of symplectic groupoids and quantization, J. Reine Angew. Math. 417 (1991), 159--189, MR 1103911.