Author(s): MICHEL VAN DEN BERGH
Let \ HH " stand for Hochschild (co)homology. In this note we show that for many rings A there exists d 2 N such that for an arbitrary A - bimodule N we have HH i ( N )= HH d − i ( N ). Such a result may be viewed as an analog of Poincar e duality. Combining this equality with a computation of Soergel allows one to com- pute the Hochschild homology of a regular minimal primitive quotient of an enveloping algebra of a semisimple Lie algebra, answering a question of Polo.