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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Noncommutative Poisson structures on orbifolds


Authors: Gilles Halbout and Xiang Tang
Journal: Trans. Amer. Math. Soc. 362 (2010), 2249-2277
MSC (2010): Primary 16E40; Secondary 58B34
Published electronically: 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 $ G$ acting on a compact manifold $ M$. Using this computation, we obtain geometric descriptions for all noncommutative Poisson structures on $ C^\infty(M)\rtimes G$ when $ M$ 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: http://dx.doi.org/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
Published electronically: December 9, 2009
Additional Notes: The second author was supported in part by NSF Grant 0604552.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.