Multiplicative structure on the Hochschild cohomology of crossed product algebras

Abstract

Consider a smooth affine algebraic variety $X$ over an algebraically closed field, and let a finite group $G$ act on it. We assume that the characteristic of the field is greater than the dimension of $X$ and the order of $G$. An explicit formula for multiplication on the Hochschild cohomology of a crossed product of $k[G]$ and $k[X]$ is given in terms of multivector fields on $X$ and $g$-invariant subvarieties of $X$ for $g\in G$.

arXiv comment9 pages; the Gerstenhaber bracket part withdrawn on 12/08/05 due to a gap in one of the proofs. Some references added

References in corpus (5)

• Deformation quantization of Poisson manifolds, I
• The Mukai pairing, II: the Hochschild-Kostant-Rosenberg isomorphism
• Multiplicative McKay correspondence in the symplectic case
• Homology of formal deformations of proper etale Lie groupoids
• Products in Hochschild cohomology and Grothendieck rings of group crossed products

Cited by in corpus (3)

• Sheaves of Twisted Cherednik Algebras as Universal Filtered Formal Deformations
• Orbifold cup products and ring structures on Hochschild cohomologies
• Hochschild cohomology of group extensions of quantum symmetric algebras