The Hochschild cohomology ring of regular maximal primitive quotients of enveloping algebras of semisimple Lie algebras

Let U be the enveloping algebra of a semisimple complex Lie algebra and m a regular maximal ideal of its center. We show that the Hochschild cohomology ring of U/mU is just the coinvariant algebra of the Weyl group. This turns out to be almost immediate if one uses localization.