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 ${\mathbb{R}}^d$ 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.

This is a contribution to the Special Issue on Deformation Quantization, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/