Bimodules, the Brauer group, Morita equivalence, and cohomology
type: Item
instance of: scholarly article
title: Bimodules, the Brauer group, Morita equivalence, and cohomology
zbMATH Open document ID: 0765.16002
DOI: 10.1016/0022-4049(92)90149-A
author: Samuel D. Schack
published in: Journal of Pure and Applied Algebra
publication date: 1993-01-16T00:00:00Z
review text: For \(k\)-algebras \(A\) and \(B\) let \(A\)-mod-\(B\) denote the category of \((A\)- \(B)\)-bimodules. A \(k\)-linear equivalence of categories \(A: A\)-mod-\(A\to B\)-mod-\(B\) is called a (weak) \(k\)-congruence if \(TA\approx B\). The author shows that many familiar Morita invariant properties (e.g. the Hochschild and cyclic cohomologies, the center) are trivially seen to be congruence invariant. The congruence is used to give an economical description of the Brauer group and to answer \textit{D. Zelinsky's} concluding question [in: Ring Theory II, Proc. 2nd Okla. Conf. 1975, 69-101 (1977; Zbl 0356.13002)].
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16D20
Mathematics Subject Classification ID: 16E40
zbMATH DE Number: 89588
zbMATH Keywords: category of \((A\)-\(B)\)-bimodules
zbMATH Keywords: equivalence of categories
zbMATH Keywords: Morita invariant
zbMATH Keywords: Hochschild and cyclic cohomologies
zbMATH Keywords: congruence invariant
zbMATH Keywords: Brauer group
reviewed by: Marek Golasiński
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 89588