First order cohomology of Banach semigroup algebras
type: Item
instance of: scholarly article
title: First order cohomology of Banach semigroup algebras
zbMATH Open document ID: 0910.46055
published in: Semigroup Forum
publication date: 1999-04-20T00:00:00Z
review text: Denoting by \(A\) a (complex) Banach algebra and by \(X\) a Banach \(A\)-bimodule, the authors show here that when \(S\) is a semigroup and \(A\) is the convolution Banach semigroup algebra \(\ell^1(S)\), it is often possible to compute the first-order cohomology group \(H^1(A, X)\), that is the space of \(X\)-valued bounded derivations modulo the inner derivations. Namely, the cases which are most interesting in this paper are \(X= A^*\) and \(X= A\) with their natural bimodule products and two other important bimodules given by \(X= (A\otimes A)^*\) and \(X= A\otimes A\), as well as bimodules associated with semigroups action on a set.
Mathematics Subject Classification ID: 46M20
Mathematics Subject Classification ID: 46H25
zbMATH DE Number: 1106585
zbMATH Keywords: Banach \(A\)-bimodule
zbMATH Keywords: convolution Banach semigroup algebra
zbMATH Keywords: first-order cohomology group
zbMATH Keywords: bimodule products
zbMATH Keywords: bimodules associated with semigroups action
author: Shannon R. Bowling
author: J. Duncan
reviewed by: Liliana Răileanu
MaRDI profile type: Publication
full work available at URL: s00233-002-7009-z
OpenAlex ID: W2001928109
DOI: 10.1007/S00233-002-7009-Z
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description: scientific article; zbMATH DE number 1106585