The Temperley-Lieb algebra at roots of unity
type: Item
instance of: scholarly article
title: The Temperley-Lieb algebra at roots of unity
zbMATH Open document ID: 0823.16004
author: Frederick M. Goodman
author: Hans Wenzl
published in: Pacific Journal of Mathematics
publication date: 1995-10-15T00:00:00Z
review text: The ascending sequences of finite dimensional algebras, given by relations (between generators) depending on one or several parameters, are considered. It is assumed that, for generic values of parameters, the algebras are semisimple. A systematic study is initiated of the structure of such algebras at the critical values of the parameters, where they cease to be semisimple. The Temperley-Lieb algebras are studied in detail; however, it is expected that the techniques used can be applied to other cases (Brauer algebras, Birman-Wenzl algebras). The main techniques used in the paper are: (i) the use of representation theory to obtain the algebraic identities which remain valid at critical values of parameters, (ii) spectral analysis for path idempotents.
reviewed by: Piotr Kosiński
Mathematics Subject Classification ID: 16D60
Mathematics Subject Classification ID: 16G99
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 17B81
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 540668
zbMATH Keywords: Brauer algebras
zbMATH Keywords: Hecke algebras
zbMATH Keywords: semisimple algebras
zbMATH Keywords: nonsemisimple algebras
zbMATH Keywords: Bratteli diagrams
zbMATH Keywords: ascending sequences of finite dimensional algebras
zbMATH Keywords: relations
zbMATH Keywords: generators
zbMATH Keywords: Temperley-Lieb algebras
zbMATH Keywords: Birman-Wenzl algebras
MaRDI profile type: Publication
full work available at URL: pjm.1993.161.307
OpenAlex ID: W2078096638
DOI: 10.2140/PJM.1993.161.307
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description: scientific article; zbMATH DE number 540668