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

Let A(n) be the nth Weyl algebra, and let G subset of SP2n(C) subset of 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 CG with respect to a filtration defined in terms of the defining representation of G. (C) 2002 Elsevier Science (USA).