Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 060, 17 pages      arXiv:0805.2409
Contribution to the Special Issue on Deformation Quantization

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

Damien Calaque and Carlo A. Rossi
Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland

Received May 23, 2008, in final form August 29, 2008; Published online September 03, 2008

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 Rd 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.

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

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