On the irreducible representations of a finite semigroup

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dc.creatorGanyushkin, Olexandr
dc.creatorMazorchuk, Volodymyr
dc.creatorSteinberg, Benjamin
dc.date2007-12-13
dc.date2007-12-19
dc.date.accessioned2026-07-07T08:50:01Z
dc.date.available2026-07-07T08:50:01Z
dc.descriptionWork of Clifford, Munn and Ponizovski{\uı} 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-Ponizovski{\uı} 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.
dc.identifierhttps://arxiv.org/abs/0712.2076
dc.identifierhttp://arxiv.org/abs/0712.2076
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144477
dc.subjectRepresentation Theory
dc.subjectGroup Theory
dc.titleOn the irreducible representations of a finite semigroup
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