Completely bounded multilinear maps and \(C^ *\)-algebraic cohomology
type: Item
instance of: scholarly article
title: Completely bounded multilinear maps and \(C^ *\)-algebraic cohomology
zbMATH Open document ID: 0646.46052
DOI: 10.1007/BF01388706
author: Erik Christensen
author: Edward G. Effros
author: Allan M. Sinclair
published in: Inventiones Mathematicae
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143510
review text: The category of completely bounded mappings is considered. The first order case concerns completely bounded derivations from a given \(C^*\)- algebra A into B(H) which are known to be inner. The higher dimensional cohomology problem is solved in the affirmative: It is shown that the cohomology groups \(H^ n_{cb}(A,B(H))\) always vanish. (The subscript refers to the completely bounded category.) Two cases are considered when the bounded cohomology groups are also shown to vanish. The conditions on the given \(C^*\)-algebra A are: (i) The weak closure \(\bar A\) is properly infinite, or alternatively, (ii) \(\bar A\simeq R{\bar \otimes}N\) with N the hyperfinite \(II_ 1\)- factor.
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46M20
zbMATH DE Number: 4054337
zbMATH Keywords: category of completely bounded mappings
zbMATH Keywords: completely bounded derivations
zbMATH Keywords: higher dimensional cohomology problem
zbMATH Keywords: bounded cohomology groups
zbMATH Keywords: \(C^ *\)-algebra
reviewed by: Palle Jorgensen
MaRDI profile type: Publication
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OpenAlex ID: W2082148563
description: scientific article; zbMATH DE number 4054337