Higher conjugations and the Yang-Baxter equation
type: Item
instance of: scholarly article
title: Higher conjugations and the Yang-Baxter equation
zbMATH Open document ID: 1014.16039
author: Sarah Whitehouse
published in: Journal of Algebra
publication date: 2002-12-16T00:00:00Z
review text: In a previous paper [Commun. Algebra 29, No. 8, 3351-3363 (2001; Zbl 0999.16034)] the author constructed actions of the symmetric groups on tensor powers of commutative or cocommutative Hopf algebras. The current paper sets these actions in the wider context of representations of the braid group and solutions of the Yang-Baxter equation, a linearization of the braid relations. The author gives a full account of the relations between braid group and symmetric group actions, between actions on \(n\)-fold and \(n-1\)-fold tensor products, and of the duality present. Remark: In the proof of Proposition 1.1 \(p^1\) should be \(p'\).
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 20F36
Mathematics Subject Classification ID: 20C30
zbMATH DE Number: 1846028
zbMATH Keywords: actions of symmetric groups
zbMATH Keywords: tensor products
zbMATH Keywords: cocommutative Hopf algebras
zbMATH Keywords: braid group actions
zbMATH Keywords: Yang-Baxter equation
reviewed by: Martin D. Crossley
MaRDI profile type: Publication
full work available at URL: jabr.2002.9146
OpenAlex ID: W1979361617
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DOI: 10.1006/JABR.2002.9146
description: scientific article; zbMATH DE number 1846028