Weak Hopf algebras with projection and weak smash bialgebra structures.
type: Item
instance of: scholarly article
title: Weak Hopf algebras with projection and weak smash bialgebra structures.
zbMATH Open document ID: 1042.16020
author: J. N. Alonso Alvarez
author: J. M. Fernández Vilaboa
author: Ramón González Rodríguez
author: M. Purificación López López
author: Emilio Villanueva Nóvoa
published in: Journal of Algebra
publication date: 2003-12-04T00:00:00Z
review text: The aim of this paper is to investigate weak Hopf algebras with projection. As a generalization of the corresponding theory of Hopf algebras, for a weak Hopf algebra \(H\), the authors introduce the category of weak Yetter-Drinfeld modules, denoted by \(^H_H\mathcal{WYD}\). For morphisms of weak Hopf algebras \(f\colon H\to B\), \(g\colon B\to H\) such that \(g\circ f=\text{id}_H\), it is verified that there exists an object \(B_H\) in \(^H_H\mathcal{WYD}\) as a weak Hopf algebra in this category with a weak Hopf algebra isomorphism \(\omega\) between \(B\) and \(B_H\bowtie H\). On the other hand, the authors give the definition of weak smash bialgebra structures and prove that, under central and cocentral conditions, the example \((B_H,H,R,S)\) can be constructed from \(B_H\) and \(H\).
Mathematics Subject Classification ID: 16T05
Mathematics Subject Classification ID: 16T10
zbMATH DE Number: 2013036
zbMATH Keywords: weak Hopf algebras
zbMATH Keywords: weak Yetter-Drinfeld modules
zbMATH Keywords: weak smash bialgebra structures
reviewed by: Fang Li
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.05.003
OpenAlex ID: W2076736564
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DOI: 10.1016/J.JALGEBRA.2003.05.003
description: scientific article; zbMATH DE number 2013036