Hochschild cohomology algebra of abelian groups
type: Item
instance of: scholarly article
title: Hochschild cohomology algebra of abelian groups
zbMATH Open document ID: 0872.16004
DOI: 10.1007/PL00000389
author: Claude Cibils
author: Andrea Solotar
published in: Archiv der Mathematik
publication date: 1997-08-19T00:00:00Z
review text: We present a direct proof of what is suggested by \textit{T. Holm}'s results [Commun. Algebra 24, No. 6, 1957-1969 (1996; Zbl 0853.16016)]: there is an isomorphism of algebras \(HH^*(kG,kG)\to kG\otimes H^*(G,k)\) where \(G\) is a finite abelian group, \(k\) a ring, \(HH^*(kG,kG)\) is the Hochschild cohomology algebra and \(H^*(G,k)\) the usual cohomology algebra. This result agrees with the well-known additive structure result in force for any group \(G\); we remark that the multiplicative structure result we have obtained is quite similar to the description of the monoidal category of Hopf bimodules over \(kG\) [given in \textit{C. Cibils}, Proc. Am. Math. Soc. 125, No. 5, 1315-1321 (1997; Zbl 0865.18005)]. This similarity leads to conjecture the structure of \(HH^*(kG,kG)\) for \(G\) a finite group.
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 1026242
zbMATH Keywords: finite Abelian groups
zbMATH Keywords: Hochschild cohomology algebras
zbMATH Keywords: monoidal categories of Hopf bimodules
MaRDI profile type: Publication
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full work available at URL: pl00000389
OpenAlex ID: W2033963432
description: scientific article; zbMATH DE number 1026242