REPRESENTATION THEORY OF FINITE SEMIGROUPS, SEMIGROUP RADICALS AND FORMAL LANGUAGE THEORY

• Type: Article in International Scientific Journal
• Date: 2009

Authors

Jorge Almeida (Author) FCUP; Stuart Margolis (Author) Other; Benjamin Steinberg (Author) Other; Mikhail Volkov (Author) Other

Journal

Title: Transactions of the American Mathematical Society

Vol. 361

Pages: 1429-1461

ISSN: 0002-9947

Publisher: American Mathematical Society

Indexing

ISI Web of Knowledge - 46 Citations

Scopus - 50 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-003-SAQ

Abstract (EN): 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 Cerny's conjecture for an important class of automata.

Language: English

Type (Professor's evaluation): Scientific