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ISSN 1088-6850(e) ISSN 0002-9947(p)

Noncommutative Poisson structures on orbifolds

Author(s): Gilles Halbout; Xiang Tang
Journal: Trans. Amer. Math. Soc. 362 (2010), 2249-2277.
MSC (2010): Primary 16E40; Secondary 58B34
Posted: December 9, 2009
MathSciNet review: 2584600
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Abstract: In this paper, we compute the Gerstenhaber bracket on the Hochschild cohomology of $C^\infty(M)\rtimes G$ for a finite group acting on a compact manifold . Using this computation, we obtain geometric descriptions for all noncommutative Poisson structures on $C^\infty(M)\rtimes G$ when is a symplectic manifold. We also discuss examples of deformation quantizations of these noncommutative Poisson structures.

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Additional Information:

Gilles Halbout
Affiliation: Institut de Mathématiques et de Mod'elisation de Montpellier I3M, UMR 5149, Université de Montpellier 2, F-34095 Montpellier cedex 5, France
Email: ghalbout@darboux.math.univ-montp2.fr

Xiang Tang
Affiliation: Department of Mathematics, Washington University, St. Louis, Missouri 63130
Email: xtang@math.wustl.edu

DOI: 10.1090/S0002-9947-09-05079-X
PII: S 0002-9947(09)05079-X
Keywords: Noncommutative Poisson structure, Hochschild cohomology, Gerstenhaber bracket, deformation
Received by editor(s): May 25, 2007
Posted: December 9, 2009
Additional Notes: The second author was supported in part by NSF Grant 0604552.
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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