Nonabelian tensor products and nonabelian homology of groups
type: Item
instance of: scholarly article
title: Nonabelian tensor products and nonabelian homology of groups
zbMATH Open document ID: 0867.20041
DOI: 10.1016/0022-4049(95)00133-6
published in: Journal of Pure and Applied Algebra
publication date: 1997-08-12T00:00:00Z
review text: Given groups \(G\) and \(A\), which act on themselves by conjugation and each of which acts on the other, the non-abelian tensor product \(G\otimes A\) was introduced by \textit{R. Brown} and \textit{J.-L. Loday} [Topology 26, 311-335 (1987; Zbl 0622.55009)]. Using the theory of non-abelian derived functors the author defines homology groups \(H_n(G,A)\) as the left-derived functors of the non-abelian tensor product \(G\otimes A\), which coincide with the classical homology groups if \(A\) is abelian. He further shows that there is a long exact sequence in non-abelian homology, which extends the sequence in low degrees of \textit{D. Guin} [J. Pure Appl. Algebra 50, No. 2, 109-137 (1988; Zbl 0653.20051)].
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 18G50
Mathematics Subject Classification ID: 18G10
zbMATH DE Number: 933078
zbMATH Keywords: nonabelian tensor products
zbMATH Keywords: nonabelian derived functors
zbMATH Keywords: homology groups
zbMATH Keywords: long exact sequences in nonabelian homology
author: N. Inassaridze
reviewed by: Manfred Kolster
MaRDI profile type: Publication
full work available at URL: 0022-4049(95)00133-6
OpenAlex ID: W2045785669
cites work: Q5566551
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cites work: Simplicial resolutions and derived functors
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description: scientific article; zbMATH DE number 933078