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

Mariano Suarez-Alvarez
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Abstract

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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Mariano Suarez-Alvarez. 2001-09-10. Algebra structure on the Hochschild cohomology of the ring of invariants of a Weyl algebra under a finite group. https://arxiv.org/abs/math/0109068

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