A left quantum group.
type: Item
instance of: scholarly article
title: A left quantum group.
zbMATH Open document ID: 1073.16033
author: Suemi Rodríguez-Romo
author: Earl J. Taft
published in: Journal of Algebra
publication date: 2005-04-21T00:00:00Z
review text: A left Hopf algebra is a bialgebra \(H\) with a left antipode \(S\), i.e. a linear map \(S\colon H\to H\) such that \(S*I=\mu\varepsilon\), where \(\varepsilon\) is the counit, \(\mu\) is the unit, \(I\) is the identity map, and \(*\) is the convolution product. A left Hopf algebra which is not a Hopf algebra was constructed by \textit{J. A. Green, W. D. Nichols} and \textit{E. J. Taft} [J. Algebra 65, 399-411 (1980; Zbl 0439.16008)]. In the paper under review, the authors construct a left Hopf algebra which is not a Hopf algebra by considering only some of the defining relations of \(\text{SL}_q(2)\). They obtain a left Hopf algebra \(H\) with the property that no left antipode of \(H\) is an algebra antimorphism.
reviewed by: Sorin Dascalescu
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16W35
zbMATH DE Number: 2159741
zbMATH Keywords: left Hopf algebras
zbMATH Keywords: quantum groups
zbMATH Keywords: quantum planes
zbMATH Keywords: bialgebras
zbMATH Keywords: left antipodes
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2005.01.002
OpenAlex ID: W2080690908
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DOI: 10.1016/J.JALGEBRA.2005.01.002
description: scientific article; zbMATH DE number 2159741