This article is cited in 3 papers

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

Damien Calaque, Carlo A. Rossi

Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland

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.

Keywords: deformation quantization; formality theorems; cap-products; Duflo isomorphism.

MSC: 16E45; 16E40; 81Q30

Received: May 23, 2008; in final form August 29, 2008; Published online September 3, 2008

Language: English

DOI: 10.3842/SIGMA.2008.060

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ArXiv: 0805.2409