Tate-Hochschild homology and cohomology of Frobenius algebras

2011/09/19 by Petter Andreas Bergh, Bergh, Petter Andreas, David A. Jorgensen +1
Mathematics · #16D50 #16E30 #16E40 #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA) #math.KT #math.RA #msc:16D50 #msc:16E30 #msc:16E40

paper · pdf · doi:10.48550/arxiv.1109.4019

26 pages, to appear in J. Noncommut. Geom

arxiv created 2011/10/07 · arxiv updated 2011/10/10

Abstract

We study Tate-Hochschild homology and cohomology for a two-sided Noetherian Gorenstein algebra. These (co)homology groups are defined for all degrees, non-negative as well as negative, and they agree with the usual Hochschild (co)homology groups for all degrees larger than the injective dimension of the algebra. We prove certain duality theorems relating the Tate-Hochschild (co)homology groups in positive degree to those in negative degree, in the case where the algebra is Frobenius. We explicitly compute all Tate-Hochschild (co)homology groups for certain classes of Frobenius algebras, namely, certain quantum complete intersections.

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