REPRESENTATION THEORY OF FINITE SEMIGROUPS, SEMIGROUP RADICALS AND FORMAL LANGUAGE THEORY / Almeida Jorge,Margolis Stuart,Steinberg Benjamin,Volkov Mikhail // TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - 2009. - V. 361, l. 3. - P. 1429-1461.

ISSN/EISSN:

0002-9947 / нет данных

Type:

Article

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 Cerny's conjecture for an important class of automata.

Author keywords:

Representation theory; radicals; language theory DECOMPOSITION TECHNIQUES; COMPLEX REPRESENTATIONS; MATRIX REPRESENTATIONS; CATEGORIES; MONOIDS; AUTOMATA; PSEUDOVARIETIES; PRODUCT; COUNTER

DOI:

нет данных

Web of Science ID:

ISI:000261255300013

Соавторы в МНС:

—

Другие поля

Поле	Значение
Publisher	AMER MATHEMATICAL SOC
Address	201 CHARLES ST, PROVIDENCE, RI 02940-2213 USA
Language	English
Article-Number	PII S0002-9947(08)04712-0
Keywords-Plus	DECOMPOSITION TECHNIQUES; COMPLEX REPRESENTATIONS; MATRIX REPRESENTATIONS; CATEGORIES; MONOIDS; AUTOMATA; PSEUDOVARIETIES; PRODUCT; COUNTER
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics
Author-Email	jalmeida@fc.up.pt margolis@math.biu.ac.il bsteinbg@math.carleton.ca Mikhail.Volkov@usu.ru
ResearcherID-Numbers	Volkov, Mikhail/F-1407-2014 Almeida, Jorge /B-8575-2015
ORCID-Numbers	Volkov, Mikhail/0000-0002-9327-243X Almeida, Jorge /0000-0002-3829-2382
Funding-Acknowledgement	Centro de Matematica da Universidade do Porto; FCT; Excellency Center; Israeli Science Foundation; NSERC; Russian Foundation for Basic Research {[}05-01-00540]
Funding-Text	The fourth author acknowledges support from the Russian Foundation for Basic Research, grant 05-01-00540.
Number-of-Cited-References	75
Usage-Count-Since-2013	2
Journal-ISO	Trans. Am. Math. Soc.
Doc-Delivery-Number	377MM