2007/02/14 by Jorge Almeida, Stuart Margolis, Benjamin Steinberg +1 · 2 citations
Mathematics · #math.GR #math.CO #math.RT
paper · pdf · doi:10.1090/s0002-9947-08-04712-0
published as Trans. Amer. Math. Soc. 361 (2009), 1429-1461
arxiv created 2007/02/14 · arxiv updated 2014/11/25
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 Černý's conjecture for an important class of automata.