Ribbon transformations, integrals, and triangular decompositions.
type: Item
instance of: scholarly article
title: Ribbon transformations, integrals, and triangular decompositions.
zbMATH Open document ID: 1103.16027
author: Yorck Sommerhäuser
published in: Journal of Algebra
publication date: 2005-04-07T00:00:00Z
review text: This paper discusses distinct facts related to integrals in Yetter-Drinfel'd Hopf algebras, i.e., Hopf algebras in the braided category of Yetter-Drinfel'd modules over a Hopf algebra. It introduces the twisted Nakayama automorphism and proves an analogue, in the Yetter-Drinfel'd context, of a formula due to \textit{D. E. Radford} for the fourth power of the antipode [Am. J. Math. 98, 333-355 (1976; Zbl 0332.16007)]. This formula is compared in an Appendix with the formula obtained by \textit{Yu. Bespalov, T. Kerler, V. Lyubashenko} and \textit{V. Turaev} [in J. Pure Appl. Algebra 148, No. 2, 113-164 (2000; Zbl 0961.16023)]. Integrals for two kinds of Hopf algebras with triangular decomposition that arise from Yetter-Drinfel'd Hopf algebras are computed, and this is applied to the case of the Frobenius-Lusztig kernel of \(sl(2)\).
reviewed by: Sonia Natale
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 18D10
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 2153372
zbMATH Keywords: Yetter-Drinfeld Hopf algebras
zbMATH Keywords: Yetter-Drinfeld modules
zbMATH Keywords: integrals
zbMATH Keywords: braided Hopf algebras
zbMATH Keywords: braided tensor categories
zbMATH Keywords: Radford formula
zbMATH Keywords: antipodes
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2004.05.001
OpenAlex ID: W1966944077
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DOI: 10.1016/J.JALGEBRA.2004.05.001
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description: scientific article; zbMATH DE number 2153372