Weak \(C\)-cleft extensions, weak entwining structures and weak Hopf algebras.
type: Item
instance of: scholarly article
title: Weak \(C\)-cleft extensions, weak entwining structures and weak Hopf algebras.
zbMATH Open document ID: 1085.16027
author: J. M. Fernández Vilaboa
author: Ramón González Rodríguez
author: J. N. Alonso Alvarez
author: Ana Belen Rodríguez Raposo
published in: Journal of Algebra
publication date: 2005-04-07T00:00:00Z
review text: The notion of weak entwining structures was introduced by \textit{S. Caenepeel} and \textit{E. De Groot} [Contemp. Math. 267, 31-54 (2000; Zbl 0978.16033)] generalizing previous work of Brzeziński and Majid. The importance of this notion is that it allows to unify the definition of several categories by putting them into the framework of `categories of entwined modules'. This paper introduces the notion of cleft extensions for weak entwining structures in a braided monoidal category with equalizers and coequalizers. It is shown that certain results in the literature, like for instance that of \textit{J. N. Alonso Álvarez} and \textit{R. González Rodríguez} [J. Algebra 281, No. 2, 731-752 (2004; Zbl 1073.16027)] on crossed products for weak Hopf algebras are particular instances of more general theorems that they obtain in the context of weak entwining structures.
reviewed by: Sonia Natale
Mathematics Subject Classification ID: 16T05
Mathematics Subject Classification ID: 18D10
zbMATH DE Number: 2153321
zbMATH Keywords: weak entwining structures
zbMATH Keywords: weak cleft extensions
zbMATH Keywords: weak Hopf algebras
zbMATH Keywords: braided monoidal categories
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2004.07.043
OpenAlex ID: W2083178693
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DOI: 10.1016/J.JALGEBRA.2004.07.043
description: scientific article; zbMATH DE number 2153321