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.