Semigroup identities in the monoid of two-by-two tropical matrices
Group Theory
2009-02-10 v1 Rings and Algebras
Abstract
The main result of the paper proves that the monoid of all 2 x 2 tropical matrices satisfies a non-trivial semigroup identity, unlike the case of matrices over infinite fields. We exploit a strong connection between the monoid of all 2 x 2 tropical matrices and the bicyclic monoid to show that a variant of Adian's identity for the bicyclic monoid holds in our case.We use generic matrices of tropical polynomials to prove our result.
Keywords
Cite
@article{arxiv.0902.1174,
title = {Semigroup identities in the monoid of two-by-two tropical matrices},
author = {Zur Izhakian and Stuart Margolis},
journal= {arXiv preprint arXiv:0902.1174},
year = {2009}
}