English

Representation Theory of Finite Semigroups over Semirings

Rings and Algebras 2010-04-13 v1 Representation Theory

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.

Keywords

Cite

@article{arxiv.1004.1660,
  title  = {Representation Theory of Finite Semigroups over Semirings},
  author = {Zur Izhakian and John Rhodes and Benjamin Steinberg},
  journal= {arXiv preprint arXiv:1004.1660},
  year   = {2010}
}