Quasitriangular pointed Hopf algebras constructed by Ore extensions.
type: Item
instance of: scholarly article
title: Quasitriangular pointed Hopf algebras constructed by Ore extensions.
zbMATH Open document ID: 1058.16034
DOI: 10.1023/B:ALGE.0000026785.03997.60
author: Adriana Nenciu
published in: Algebras and Representation Theory
publication date: 2004-08-19T00:00:00Z
review text: The author considers a class of complex finite-dimensional pointed Hopf algebras which were constructed by \textit{M. Beattie}, \textit{S. Dăscălescu} and \textit{L. Grünenfelder} [J. Algebra 225, No. 2, 743-770 (2000; Zbl 0948.16026)], and determines which ones are quasitriangular. This class includes the Taft Hopf algebras, a class constructed by \textit{D. E. Radford} [Lect. Notes Pure Appl. Math. 158, 205-266 (1994; Zbl 0841.57044)], who determined which of his self-dual Hopf algebras are quasitriangular, a class constructed by \textit{F. Panaite} and \textit{F. Van Oystaeyen} [Commun. Algebra 27, No. 10, 4929-4942 (1999; Zbl 0943.16019)], and a generalization of this class by the author [Commun. Algebra 29, No. 8, 3419-3432 (2001; Zbl 0991.16035)]. For those which are quasitriangular, she determines their ribbon elements, and also the quasi-ribbon elements of their Drinfeld doubles. Reviewer's note: There is a confusing statement in the introduction which seems to say that Radford's self-dual Hopf algebras are all quasitriangular. This is not so. In particular, the Taft Hopf algebras are self-dual and they are not quasitriangular for \(n>2\). This is all sorted out correctly in Remark 3.5 after Theorem 3.4.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 57T05
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 2093330
zbMATH Keywords: quasitriangular Hopf algebras
zbMATH Keywords: \(R\)-matrix
zbMATH Keywords: ribbon elements
zbMATH Keywords: Drinfeld doubles
zbMATH Keywords: Taft algebras
reviewed by: Earl J. Taft
MaRDI profile type: Publication
full work available at URL: b:alge.0000026785.03997.60
OpenAlex ID: W2025426489
description: scientific article; zbMATH DE number 2093330