Representation theory of finite semigroups, semigroup radicals and formal language theory
| Venue: | in preparation. COUNTING AND MATRIX REPRESENTATIONS 11 |
| Citations: | 11 - 8 self |
BibTeX
@INPROCEEDINGS{Almeida_representationtheory,
author = {Jorge Almeida and Stuart Margolis and Benjamin Steinberg},
title = {Representation theory of finite semigroups, semigroup radicals and formal language theory},
booktitle = {in preparation. COUNTING AND MATRIX REPRESENTATIONS 11},
year = {}
}
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Abstract
Abstract. In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are given to obtain many new results, as well as easier proofs of several results in the literature, involving: triangularizability of finite semigroups; which semigroups have (split) basic semigroup algebras, two-sided semidirect product decompositions of finite monoids; unambiguous products of rational languages; products of rational languages with counter; and Čern´y’s conjecture for an important class of automata.
