Algebra Structure on the Hochschild Cohomology of the Ring of Invariants of a Weyl Algebra under a Finite Group,

Let An be the nth Weyl algebra, and let G Sp2n( ) Aut(An) be a finite group of linear automorphisms of An. In this paper, we compute the multiplicative structure on the Hochschild cohomology HH•(AGn) of the algebra of invariants of G. We prove that, as a graded algebra, HH•(AGn) is isomorphic to the graded algebra associated to the center of the group algebra G with respect to a filtration defined in terms of the defining representation of G.