Algebra structure on the Hochschild cohomology of the ring of invariants of a Weyl algebra under a finite group

Details Algebra structure on the Hochschild cohomology of the ring of invariants of a Weyl algebra under a finite group Algebra structure on the Hochschild cohomology of the ring of invariants of a Weyl algebra under a finite group

2001-09-10

arxiv.org/abs/math/0109068v1

J. Algebra 248 (2002), pp. 291--306.

Mathematics

K-Theory and Homology

13 pages

Scientific paper

Let $A_n$ be the $n$-th Weyl algebra, and let $G\subset\Sp_{2n}(\C)\subset\Aut(A_n)$ be a finite group of linear automorphisms of $A_n$. In this paper we compute the multiplicative structure on the Hochschild cohomology $\HH^*(A_n^G)$ of the algebra of invariants of $G$. We prove that, as a graded algebra, $\HH^*(A_n^G)$ is isomorphic to the graded algebra associated to the center of the group algebra $\C G$ with respect to a filtration defined in terms of the defining representation of $G$.

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