Generalized table algebras

Z. Arad, E. Fisman, M. Muzychuk

Research output: Contribution to journalArticlepeer-review

93 Scopus citations

Abstract

A table algebra was defined in [1] in order to consider in a uniform way the common properties of conjugacy classes and irreducible characters. Non-commutative table algebras were introduced in [5]. They generalize properties of such well-known objects as coherent and Hecke algebras. Here we extend the main definition of a non-commutative table algebra by letting the ground field be an integral domain. We call these algebras generalized table algebras (GT-algebras, in brief). It is worth mentioning that this class of algebras includes generic Hecke-Iwahori algebras of finite Coxeter groups. We develop the general theory for this type of algebras which includes their representation theory and theory of closed subsets. We also study the properties of primitive integral table algebras.

Original languageEnglish
Pages (from-to)29-60
Number of pages32
JournalIsrael Journal of Mathematics
Volume114
DOIs
StatePublished - 1 Jan 1999
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)

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