Treffer: Quasitriangular Pointed Hopf Algebras Constructed by Ore Extensions: Quasitriangular pointed Hopf algebras constructed by Ore extensions.

Title:
Quasitriangular Pointed Hopf Algebras Constructed by Ore Extensions: Quasitriangular pointed Hopf algebras constructed by Ore extensions.
Authors:
Adriana Nenciu
Source:
Algebras and Representation Theory. 7:159-172
Publisher Information:
Springer Science and Business Media LLC, 2004.
Publication Year:
2004
Subject Terms:
Drinfeld doubles, Taft algebras, Ordinary and skew polynomial rings and semigroup rings, Hopf algebras (aspects of homology and homotopy of topological groups), ribbon elements, quasitriangular Hopf algebras, 0101 mathematics, Quantum groups and related algebraic methods applied to problems in quantum theory, 01 natural sciences, \(R\)-matrix, Hopf algebras (associative rings and algebras)
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Language:
English
ISSN:
1572-9079
1386-923X
DOI:
10.1023/b:alge.0000026785.03997.60
Access URL:
https://zbmath.org/2093330
https://doi.org/10.1023/b:alge.0000026785.03997.60
https://link.springer.com/article/10.1023/B:ALGE.0000026785.03997.60
Rights:
Springer Nature TDM
Accession Number:
edsair.doi.dedup.....fb616c19b0192edd7fb2d3176231f820
Database:
OpenAIRE

Weitere Informationen

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.