Xu, Ping
Morita equivalence and symplectic realizations of Poisson manifolds
Annales scientifiques de l'École Normale Supérieure, Série 4 : Tome 25 (1992) no. 3 , p. 307-333
Zbl 0767.58014 | MR 93f:58084
doi : 10.24033/asens.1652
URL stable : http://www.numdam.org/item?id=ASENS_1992_4_25_3_307_0

Bibliographie

[CDW] A. Coste, P. Dazord and A. Weinstein, Groupoïdes Symplectiques (Publications du Département de Mathématiques, Université Claude-Bernard, Lyon-I, 1987). | Numdam | MR 90g:58033 | Zbl 0668.58017

[Co] F. Combes, Crossed Products and Morita Equivalence (Proc. London Math. Soc., 3, Vol. 49, 1984, pp. 289-306). MR 86c:46081 | Zbl 0521.46058

[CMW] R. E. Curto, P. S. Muhly and D. P. Williams, Cross Products of Strongly Morita Equivalent C*-Algebras (Proc. Am. Math. Soc., Vol. 90, No. 4, 1984, pp. 528-530). MR 85i:46083 | Zbl 0508.22012

[D1] P. Dazord, Groupoïdes Symplectiques et Troisième Théorème de Lie "Non Linéaire" (Lect. Notes Math., C. ALBERT Ed., No. 1416, 1990. MR 91i:58169 | Zbl 0702.58023

[D2] P. Dazord, Réalisations Isotropes de Libermann (Publ. Dept. Math. Lyon, 1989).

[KaO] M. V. Karasev, Quantization of Nonlinear Lie-Poisson Brackets in Quasiclassical Approximation, Preprint ITF-85-72R [Inst. Theoret. Phys. Acad. Sci. Ukrainian S.S.R., Kiev, 1985 (in Russian)].

[Ka] M. V. Karasev, Analogues of Objects of the Theory of Lie Groups for Nonlinear Poisson Brackets (Math. U.S.S.R. Izvestiya, Vol. 28, 1987, pp. 497-527). Zbl 0624.58007

[KaMa] M. V. Karasev and V. P. Maslov, Global Asymptotic Operators of the Regular Representation (Soviet Math. Dokl., Vol. 23, 1981, pp. 228-232). MR 82e:81020 | Zbl 0476.58025

[KM] P. S. Krishnaprasad and J. Marsden, Hamiltonian Structures and Stability for Rigid Bodies with Flexible Attachments (I. Arch. Rat. Mech. Anal., Vol. 98, No. 1, 1987, pp. 71-93). MR 87m:58084 | Zbl 0624.58010

[Ku] N. H. Kuiper, The Homotopy Type of the Unitary Group of Hilbert Space (Topology, Vol. 3, 1965, pp. 19-30). MR 31 #4034 | Zbl 0129.38901

[L] A. Lichnerowicz, Les Variétés de Poisson et Leurs Algèbres de Lie Associées (J. Diff. Geom., Vol. 12, 1977, pp. 253-300). MR 58 #18565 | Zbl 0405.53024

[LW] J.-H. Lu and A. Weinstein, Groupoïdes Symplectiques Doubles des Groupes de Lie-Poisson (C. R. Acad. Sci. Paris, T. 309, Série I, 1989, pp. 951-954). MR 91i:58045 | Zbl 0701.58025

[M1] K. Mackenzie, Lie Groupoids and Lie Algebroids in Differential Geometry (L.M.S. Lect. Notes Series, No. 124, Cambridge Univ. Press, 1987). MR 89g:58225 | Zbl 0683.53029

[MW] J. Marsden and A. Weinstein, Reduction of Symplectic Manifolds with Symmetry (Rep. Math. Phys., Vol. 5, 1974, pp. 121-129). MR 53 #6633 | Zbl 0327.58005

[MiW] K. Mikami and A. Weinstein, Moments and Reduction for Symplectic Groupoid Ations (Publ. R.I.M.S. Kyoto Univ., Vol. 24, 1998, pp. 121-140). MR 90c:58060 | Zbl 0659.58016

[Pe] C. K. Pederson, C*-Algebras and their Automorphism Groups, Academic Press, London, New York, 1979. Zbl 0416.46043

[Ren] J. Renault, A Groupoid Approach to C*-Algebras (Lect. Notes Math., No. 793, 1980). MR 82h:46075 | Zbl 0433.46049

[Rie1] M. A. Rieffel, Induced Representations of C*-Algebras (Adv. Math., Vol. 13, 1974, pp. 176-257). MR 50 #5489 | Zbl 0284.46040

[Rie2] M. A. Rieffel, Morita Equivalence for Operator Algebras (Proc. Symp. Pure Math., Vol. 38, 1982, pp. 285-298). MR 84k:46045 | Zbl 0541.46044

[Rie3] M. A. Rieffel, Applications of Strong Morita Equivalence to Transformation Group C*-Algebras (Proc. Symp. Pure Math., Vol. 38, 1982, pp. 299-310). MR 84k:46046 | Zbl 0526.46055

[Rie4] M. A. Rieffel, Proper Actions of Groups on C*-Algebras, preprint.

[W1] A. Weinstein, The Local Structure of Poisson Manifolds (J. Diff. Geom., Vol. 18, 1983, pp. 523-557). MR 86i:58059 | Zbl 0524.58011

[W2] A. Weinstein, Symplectic Groupoids and Poisson Manifolds (Bull. Am. Math. Soc., Vol. 16, 1987, pp. 101-104). MR 88c:58019 | Zbl 0618.58020

[W3] A. Weinstein, Blowing up Realizations of Heisenberg-Poisson Manifolds (Bull. Sci. Math., 2e Série, Vol. 113, 1989, pp. 381-406). MR 91b:58082 | Zbl 0693.58004

[W4] A. Weinstein, Poisson Geometry of the Principal Series and Nonlinearizable Structures (J. Diff. Geom., Vol. 25, 1987, pp. 55-73). MR 88g:58071 | Zbl 0592.58024

[W5] A. Weinstein, The Groupoid for a Bundle of Symplectic Manifolds, private communication.

[WX] A. Weinstein and P. Xu, Extensions of Symplectic Groupoids and Quantization (J. Reine Angew. Math., Vol. 417, 1991, pp. 159-189). MR 92k:58094 | Zbl 0722.58021

[X1] P. Xu, Morita Equivalent Symplectic Groupoids (Séminaire Sud-Rhodanien, Berkeley (Symplectic geometry, groupoids, and integrable systems) Springer-M.S.R.I. publications, 1991, pp. 291-311). MR 92i:46086 | Zbl 0733.58013

[X2] P. Xu, Morita Equivalence of Poisson Manifolds (Commun. Math. Phys., Vol. 142, 1991, pp. 493-509). MR 93a:58069 | Zbl 0746.58034