Shoikhet's Conjecture and Duflo Isomorphism on (Co)Invariants

Abstract

In this paper we prove a conjecture of B. Shoikhet. This conjecture states that the tangent isomorphism on homology, between the Poisson homology associated to a Poisson structure on R^d and the Hochschild homology of its quantized star-product algebra, is an isomorphism of modules over the (isomorphic) respective cohomology algebras. As a consequence, we obtain a version of the Duflo isomorphism on coinvariants.

Keywords

• deformation quantization
• formality theorems
• cap-products
• Duflo isomorphism