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

2001/09/10 by Mariano Suarez-Alvarez
Mathematics · #math.KT

paper · pdf

published as J. Algebra 248 (2002), pp. 291--306. · 13 pages

arxiv created 2001/09/10 · arxiv updated 2009/11/30

Abstract

Let A_n be the n-th Weyl algebra, and let G⊂\Sp_2n(\C)⊂\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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