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Noncommutative Poisson structures on Orbifolds

Gilles Halbout·Xiang Tang
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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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Gilles Halbout, Xiang Tang. 2009-05-21. Noncommutative Poisson structures on Orbifolds. https://arxiv.org/abs/math/0606436

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