Noncommutative Poisson structures on orbifolds

Halbout, Gilles; Tang, Xiang

doi:10.1090/S0002-9947-09-05079-X

Noncommutative Poisson structures on orbifolds
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by Gilles Halbout and Xiang Tang

Trans. Amer. Math. Soc. 362 (2010), 2249-2277

DOI: https://doi.org/10.1090/S0002-9947-09-05079-X

Published electronically: December 9, 2009

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Abstract:

In this paper, we compute the Gerstenhaber bracket on the Hoch-schild 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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