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arXiv · 1004.1660

Representation Theory of Finite Semigroups over Semirings

Zur Izhakian·John Rhodes·Benjamin Steinberg
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Abstract

We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the results for a field. Special attention is paid to the boolean semiring, where we also characterize the simple representations and introduce the beginnings of a character theory.

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Zur Izhakian, John Rhodes, Benjamin Steinberg. 2010-04-09. Representation Theory of Finite Semigroups over Semirings. https://arxiv.org/abs/1004.1660

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