A relation between Hochschild homology and cohomology for Gorenstein rings
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- by Michel van den Bergh
- Proc. Amer. Math. Soc. 126 (1998), 1345-1348
- DOI: https://doi.org/10.1090/S0002-9939-98-04210-5
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Erratum: Proc. Amer. Math. Soc. 130 (2002), 2809-2810.
Abstract:
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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Bibliographic 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
- Received by editor(s): November 5, 1996
- Additional Notes: The author is a senior researcher at the NFWO
- Communicated by: Lance W. Small
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 1345-1348
- MSC (1991): Primary 16E40
- DOI: https://doi.org/10.1090/S0002-9939-98-04210-5
- MathSciNet review: 1443171