Morita equivalence and symplectic realizations of Poisson manifolds

Ping Xu

Annales scientifiques de l'École Normale Supérieure (1992)

  • Volume: 25, Issue: 3, page 307-333
  • ISSN: 0012-9593

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Xu, Ping. "Morita equivalence and symplectic realizations of Poisson manifolds." Annales scientifiques de l'École Normale Supérieure 25.3 (1992): 307-333. <http://eudml.org/doc/82321>.

@article{Xu1992,
author = {Xu, Ping},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {symplectic structures; Lie groupoids; groupoid equivalence; Poisson structures; symplectic groupoids; Morita equivalent},
language = {eng},
number = {3},
pages = {307-333},
publisher = {Elsevier},
title = {Morita equivalence and symplectic realizations of Poisson manifolds},
url = {http://eudml.org/doc/82321},
volume = {25},
year = {1992},
}

TY - JOUR
AU - Xu, Ping
TI - Morita equivalence and symplectic realizations of Poisson manifolds
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1992
PB - Elsevier
VL - 25
IS - 3
SP - 307
EP - 333
LA - eng
KW - symplectic structures; Lie groupoids; groupoid equivalence; Poisson structures; symplectic groupoids; Morita equivalent
UR - http://eudml.org/doc/82321
ER -

References

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  1. [CDW] A. COSTE, P. DAZORD and A. WEINSTEIN, Groupoïdes Symplectiques (Publications du Département de Mathématiques, Université Claude-Bernard, Lyon-I, 1987). Zbl0668.58017MR90g:58033
  2. [Co] F. COMBES, Crossed Products and Morita Equivalence (Proc. London Math. Soc., 3, Vol. 49, 1984, pp. 289-306). Zbl0521.46058MR86c:46081
  3. [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). Zbl0508.22012MR85i:46083
  4. [D1] P. DAZORD, Groupoïdes Symplectiques et Troisième Théorème de Lie "Non Linéaire" (Lect. Notes Math., C. ALBERT Ed., No. 1416, 1990. Zbl0702.58023MR91i:58169
  5. [D2] P. DAZORD, Réalisations Isotropes de Libermann (Publ. Dept. Math. Lyon, 1989). 
  6. [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)]. 
  7. [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). Zbl0624.58007
  8. [KaMa] M. V. KARASEV and V. P. MASLOV, Global Asymptotic Operators of the Regular Representation (Soviet Math. Dokl., Vol. 23, 1981, pp. 228-232). Zbl0476.58025MR82e:81020
  9. [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). Zbl0624.58010MR87m:58084
  10. [Ku] N. H. KUIPER, The Homotopy Type of the Unitary Group of Hilbert Space (Topology, Vol. 3, 1965, pp. 19-30). Zbl0129.38901MR31 #4034
  11. [L] A. LICHNEROWICZ, Les Variétés de Poisson et Leurs Algèbres de Lie Associées (J. Diff. Geom., Vol. 12, 1977, pp. 253-300). Zbl0405.53024MR58 #18565
  12. [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). Zbl0701.58025MR91i:58045
  13. [M1] K. MACKENZIE, Lie Groupoids and Lie Algebroids in Differential Geometry (L.M.S. Lect. Notes Series, No. 124, Cambridge Univ. Press, 1987). Zbl0683.53029MR89g:58225
  14. [MW] J. MARSDEN and A. WEINSTEIN, Reduction of Symplectic Manifolds with Symmetry (Rep. Math. Phys., Vol. 5, 1974, pp. 121-129). Zbl0327.58005MR53 #6633
  15. [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). Zbl0659.58016MR90c:58060
  16. [Pe] C. K. PEDERSON, C*-Algebras and their Automorphism Groups, Academic Press, London, New York, 1979. Zbl0416.46043
  17. [Ren] J. RENAULT, A Groupoid Approach to C*-Algebras (Lect. Notes Math., No. 793, 1980). Zbl0433.46049MR82h:46075
  18. [Rie1] M. A. RIEFFEL, Induced Representations of C*-Algebras (Adv. Math., Vol. 13, 1974, pp. 176-257). Zbl0284.46040MR50 #5489
  19. [Rie2] M. A. RIEFFEL, Morita Equivalence for Operator Algebras (Proc. Symp. Pure Math., Vol. 38, 1982, pp. 285-298). Zbl0541.46044MR84k:46045
  20. [Rie3] M. A. RIEFFEL, Applications of Strong Morita Equivalence to Transformation Group C*-Algebras (Proc. Symp. Pure Math., Vol. 38, 1982, pp. 299-310). Zbl0526.46055MR84k:46046
  21. [Rie4] M. A. RIEFFEL, Proper Actions of Groups on C*-Algebras, preprint. 
  22. [W1] A. WEINSTEIN, The Local Structure of Poisson Manifolds (J. Diff. Geom., Vol. 18, 1983, pp. 523-557). Zbl0524.58011MR86i:58059
  23. [W2] A. WEINSTEIN, Symplectic Groupoids and Poisson Manifolds (Bull. Am. Math. Soc., Vol. 16, 1987, pp. 101-104). Zbl0618.58020MR88c:58019
  24. [W3] A. WEINSTEIN, Blowing up Realizations of Heisenberg-Poisson Manifolds (Bull. Sci. Math., 2e Série, Vol. 113, 1989, pp. 381-406). Zbl0693.58004MR91b:58082
  25. [W4] A. WEINSTEIN, Poisson Geometry of the Principal Series and Nonlinearizable Structures (J. Diff. Geom., Vol. 25, 1987, pp. 55-73). Zbl0592.58024MR88g:58071
  26. [W5] A. WEINSTEIN, The Groupoid for a Bundle of Symplectic Manifolds, private communication. 
  27. [WX] A. WEINSTEIN and P. XU, Extensions of Symplectic Groupoids and Quantization (J. Reine Angew. Math., Vol. 417, 1991, pp. 159-189). Zbl0722.58021MR92k:58094
  28. [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). Zbl0733.58013MR92i:46086
  29. [X2] P. XU, Morita Equivalence of Poisson Manifolds (Commun. Math. Phys., Vol. 142, 1991, pp. 493-509). Zbl0746.58034MR93a:58069

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