Representation Theory of Finite Semigroups, Semigroup Radicals and Formal Language Theory
Group Theory
2014-11-25 v1 Combinatorics
Representation Theory
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 \v{C}ern\'y's conjecture for an important class of automata.
Keywords
Cite
@article{arxiv.math/0702400,
title = {Representation Theory of Finite Semigroups, Semigroup Radicals and Formal Language Theory},
author = {Jorge Almeida and Stuart Margolis and Benjamin Steinberg and Mikhail Volkov},
journal= {arXiv preprint arXiv:math/0702400},
year = {2014}
}