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Generalized table algebras

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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 algebrasgeneralized 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.

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Authors and Affiliations

  1. Department of Mathematics & Computer Science, Bar-Ilan University, 52900, Ramat-Gan, Israel

    Z. Arad, E. Fisman & M. Muzychuk

Authors
  1. Z. Arad
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  2. E. Fisman
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  3. M. Muzychuk
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Correspondence to Z. Arad.

Additional information

This research was done at the Gelbart and Minerva Foundations through the Emmy Noether Research Institute for Mathematical Science at Bar-Ilan University. The authors wish to thank these institutions for their support.

This author was partially supported by the Israeli Ministry of Absorption.

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Arad, Z., Fisman, E. & Muzychuk, M. Generalized table algebras. Isr. J. Math. 114, 29–60 (1999). https://doi.org/10.1007/BF02785571

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  • DOI: https://doi.org/10.1007/BF02785571

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