Noncommutative Poisson structures on Orbifolds

Abstract

In this paper, we compute the Gerstenhaber bracket on the Hoch-schild cohomology of $C^{\infty }(M)⋊G$ for a finite group $G$ acting on a compact manifold $M$. Using this computation, we obtain geometric descriptions for all noncommutative Poisson structures on $C^{\infty }(M)⋊G$ when $M$ is a symplectic manifold. We also discuss examples of deformation quantizations of these noncommutative Poisson structures.

28 pages