A lot of quasitriangular group-cograded multiplier Hopf algebras.
type: Item
instance of: scholarly article
title: A lot of quasitriangular group-cograded multiplier Hopf algebras.
zbMATH Open document ID: 1261.16030
author: Shuanhong Wang
author: Tao Yang
published in: Algebras and Representation Theory
publication date: 2012-07-03T00:00:00Z
review text: Group cograded multiplier Hopf algebras and the quasitriangular condition on them were defined by \textit{A. T. Abd El-Hafez, L. Delvaux} and \textit{A. Van Daele} [Algebr. Represent. Theory 10, No. 1, 77-95 (2007; Zbl 1129.16027)] and \textit{L. Delvaux, A. Van Daele} and \textit{S.-H. Wang} [J. Algebra 289, No. 2, 484-514 (2005; Zbl 1079.16022)]. The aim of the paper under review is to construct new examples of quasitriangular group-cograded multiplier Hopf algebras. For this purpose, it is introduced the concept of a \(\sigma\)-compatible pairing associated to regular multiplier Hopf algebras \(A\) and \(B\), and to a multiplier Hopf dual pairing \(\sigma\). In such a framework, a twisted double group-cograded multiplier Hopf algebra is constructed, and it is shown that it has a quasitriangular structure in the case where there is a canonical multiplier in \(M(B\otimes A)\). Examples in the particular case of usual Hopf algebras are given to illustrate the construction.
reviewed by: Sorin Dascalescu
Mathematics Subject Classification ID: 16T05
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 16T20
zbMATH DE Number: 6052421
zbMATH Keywords: quasitriangular multiplier Hopf algebras
zbMATH Keywords: twisted doubles
zbMATH Keywords: group-cograded multiplier Hopf algebras
zbMATH Keywords: compatible pairings
zbMATH Keywords: group cogradings
zbMATH Keywords: regular multiplier Hopf algebras
MaRDI profile type: Publication
full work available at URL: s10468-010-9259-x
OpenAlex ID: W2100779127
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DOI: 10.1007/S10468-010-9259-X
description: scientific article; zbMATH DE number 6052421