A relation between Hochschild homology and cohomology for Gorenstein rings
Author:
Michel van den Bergh
Journal:
Proc. Amer. Math. Soc. 126 (1998), 1345-1348
MSC (1991):
Primary 16E40
DOI:
https://doi.org/10.1090/S0002-9939-98-04210-5
Erratum:
Proc. Amer. Math. Soc. 130 (2002), 2809-2810.
MathSciNet review:
1443171
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Abstract | References | Similar Articles | Additional Information
Let “$HH$” stand for Hochschild (co)homology. In this note we show that for many rings $A$ there exists $d\in \mathbb {N}$ 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 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.
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Additional Information
Michel van den Bergh
Affiliation:
Departement WNI, Limburgs Universitair Centrum, Universitaire Campus, Building D, 3590 Diepenbeek, Belgium
MR Author ID:
176980
Email:
vdbergh@luc.ac.be
Keywords:
Hochschild homology,
Gorenstein rings
Received by editor(s):
November 5, 1996
Additional Notes:
The author is a senior researcher at the NFWO
Communicated by:
Lance W. Small
Article copyright:
© Copyright 1998
American Mathematical Society