On the semi-simplicity of cyclotomic Temperley-Lieb algebras.
type: Item
instance of: scholarly article
title: On the semi-simplicity of cyclotomic Temperley-Lieb algebras.
zbMATH Open document ID: 1084.16007
author: Hebing Rui
author: Changchang Xi
author: Weihua Yu
published in: Michigan Mathematical Journal
publication date: 2005-07-13T00:00:00Z
review text: The algebras in the title have been introduced by the first two authors [Comment. Math. Helv. 79, No. 2, 427--450 (2004; Zbl 1068.16012)]. Here, they completely determine when these algebras are semisimple. The techniques are similar to those used recently for Brauer algebras and their generalisations [\textit{W. F. Doran IV, P. J. Hanlon} and \textit{D. B. Wales}, J. Algebra 211, No. 2, 647--685 (1999; Zbl 0944.16002), \textit{H. Rui} and \textit{W. Yu}, J. Algebra 277, No. 1, 187--221 (2004; Zbl 1068.16013)]; branching rules, and induction and restriction between algebras indexed by \(n\) or \(n+2\), respectively.
reviewed by: Steffen Koenig
Mathematics Subject Classification ID: 16G10
Mathematics Subject Classification ID: 16D60
Mathematics Subject Classification ID: 16S99
Mathematics Subject Classification ID: 20C08
Mathematics Subject Classification ID: 20C30
zbMATH DE Number: 2187046
zbMATH Keywords: cyclotomic Temperley-Lieb algebras
zbMATH Keywords: cellular algebras
zbMATH Keywords: Hecke algebras
zbMATH Keywords: cyclotomic Brauer algebras
zbMATH Keywords: simple modules
zbMATH Keywords: cell modules
zbMATH Keywords: branching rules
zbMATH Keywords: semisimplicity
zbMATH Keywords: partition algebras
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1114021086
OpenAlex ID: W1964774013
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DOI: 10.1307/MMJ/1114021086
description: scientific article; zbMATH DE number 2187046