Noncommutative Poisson structures on Orbifolds

Details Noncommutative Poisson structures on Orbifolds Noncommutative Poisson structures on Orbifolds

2006-06-19

arxiv.org/abs/math/0606436v3

Mathematics

Quantum Algebra

28 pages

Scientific paper

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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