Hochschild cohomology of quantized symplectic orbifolds and the Chen-Ruan cohomology

2004/10/31 by Vasiliy Dolgushev, Pavel Etingof
Mathematics · Physics and Astronomy · #math.QA #hep-th #math.KT #msc:16E40 #msc:53D55

paper · pdf

published as Int. Math. Res. Not. 2005, no. 27, 1657-1688. · 25 pages, no figures

arxiv created 2004/12/07 · arxiv updated 2009/12/01

Abstract

We prove the additive version of the conjecture proposed by Ginzburg and Kaledin. This conjecture states that if X/G is an orbifold modeled on a quotient of a smooth affine symplectic variety X (over C) by a finite group G⊂ Aut(X) and A is a G-stable quantum algebra of functions on X then the graded vector space HH(A^G) of the Hochschild cohomology of the algebra A^G of invariants is isomorphic to the graded vector space H_CR(X/G)((h)) of the Chen-Ruan (stringy) cohomology of the orbifold X/G.

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