Cellular algebras
type: Item
instance of: scholarly article
title: Cellular algebras
zbMATH Open document ID: 0853.20029
DOI: 10.1007/BF01232365
published in: Inventiones Mathematicae
publication date: 1997-01-06T00:00:00Z
full work available at URL: https://eudml.org/doc/144334
review text: The authors define a class of associative algebras (``cellular'') by means of multiplicative properties of a basis, show that they have cell representations whose structure depends on certain invariant bilinear forms, and then obtain a general description of their irreducible representations and block theory as well as criteria for semisimplicity. These concepts are used to discuss the Brauer centraliser algebras, the Ariki-Koike algebras and the Temperley-Lieb and Jones algebras.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 20C30
zbMATH DE Number: 871761
zbMATH Keywords: associative algebras
zbMATH Keywords: cell representations
zbMATH Keywords: invariant bilinear forms
zbMATH Keywords: irreducible representations
zbMATH Keywords: semisimplicity
zbMATH Keywords: Brauer centralizer algebras
zbMATH Keywords: Ariki-Koike algebras
zbMATH Keywords: Temperley-Lieb algebras
zbMATH Keywords: Jones algebras
author: John J. Graham
author: Gus I. Lehrer
reviewed by: Chiu Sen
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 871761