Hochshild (co)homology of certain algebras of invariant differential operators

Jacques Alev

Abstract: Let g be a finite dimensional simple Lie algebra over the complex numbers, h a Cartan subalgebra, W the Weyl group and A the W-invariant differential operators over h. We compute the Hochschild homology of A and by a duality argument the Hochschild cohomology as well. The result follows from a general statement concerning the invariant algebra of the n'th Weyl algebra under the action of finite groups of linear automorphisms.

created Thu Jun 1 13:09:33 PDT 2000