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On the irreducible representations of a finite semigroup
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. (Algebra)
2009 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 137, no 11, 3585-3592 p.Article in journal (Refereed) Published
Abstract [en]

Work of Clifford, Munn and Ponizovskii parameterized the irreducible   representations of a finite semigroup in terms of the irreducible   representations of its maximal subgroups. Explicit constructions of the   irreducible representations were later obtained independently by Rhodes   and Zalcstein and by Lallement and Petrich. All of these approaches   make use of Rees's theorem characterizing 0-simple semigroups up to   isomorphism. Here we provide a short modern proof of the   Clifford-Munn-Ponizovskii result based on a lemma of J. A. Green, which   allows us to circumvent the theory of 0-simple semigroups. A novelty of   this approach is that it works over any base ring.

Place, publisher, year, edition, pages
2009. Vol. 137, no 11, 3585-3592 p.
Keyword [en]
Representations, simple modules, semigroups
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-119588DOI: 10.1090/S0002-9939-09-09857-8ISI: 000271236000005OAI: oai:DiVA.org:uu-119588DiVA: diva2:300518
Available from: 2010-02-26 Created: 2010-02-26 Last updated: 2017-12-12Bibliographically approved

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