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Journal Article
A Relation between Hochschild Homology and Cohomology for Gorenstein Rings
Michel van den Bergh
Proceedings of the American Mathematical Society
Vol. 126, No. 5 (May, 1998), pp. 1345-1348
Published
by: American Mathematical Society
https://www.jstor.org/stable/118786
Page Count: 4
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Topics: Automorphisms, Mathematical rings, Mathematical theorems, Quotients, Commutativity
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Abstract
Let "H H" stand for Hochschild (co)homology. In this note we show that for many rings A there exists d ∈ N such that for an arbitrary A-bimodule N we have HHi(N) = HHd-i(N). Such a result may be viewed as an analog of Poincaré duality. Combining this equality with a computation of Soergel allows one to compute the Hochschild homology of a regular minimal primitive quotient of an enveloping algebra of a semisimple Lie algebra, answering a question of Polo.
Proceedings of the American Mathematical Society
© 1998 American Mathematical Society