The cohomology group of weak entwining structure.
type: Item
instance of: scholarly article
title: The cohomology group of weak entwining structure.
zbMATH Open document ID: 1135.16008
author: Ling Jia
author: Fang Li
published in: Science in China. Series A
publication date: 2007-09-10T00:00:00Z
review text: Weak entwining structures have been introduced by the reviewer and De Groot, and generalize classical entwining structures. In this note, Hochschild cohomology associated to a weak entwining structure \((A,C,\psi)\) with values in an \(A\)-bimodule \(M\) is introduced. It is well-known that a certain direct factor \(\overline{A\otimes C}\) of \(A\otimes C\) is an \(A\)-coring. The main result states that \(\overline{A\otimes C}\) is projective as an \(A\)-bimodule if and only if the first Hochschild cohomology group \(H^1_\psi(A,M)=0\) for every \(A\)-bimodule \(M\). The authors then consider the special case where the weak entwining structure is associated to a weak coalgebra Galois extension.
reviewed by: Stefaan Caenepeel
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 5189107
zbMATH Keywords: weak entwining structures
zbMATH Keywords: Hochschild cohomology groups
zbMATH Keywords: weak coalgebras
zbMATH Keywords: Galois extensions
MaRDI profile type: Publication
full work available at URL: s11425-007-0005-8
OpenAlex ID: W971106436
cites work: Modules over weak entwining structures
cites work: Weak corings
cites work: On modules associated to coalgebra Galois extensions
cites work: Weak Hopf algebras. I: Integral theory and \(C^*\)-structure
cites work: The cohomology structure of an algebra entwined with a coalgebra
cites work: On the cohomology groups of an associative algebra
DOI: 10.1007/S11425-007-0005-8
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description: scientific article; zbMATH DE number 5189107