Semigroups embeddable in hyperplane face monoids
Group Theory
2013-01-01 v1 Combinatorics
Rings and Algebras
Abstract
The left regular band structure on a hyperplane arrangement and its representation theory provide an important connection between semigroup theory and algebraic combinatorics. A finite semigroup embeds in a real hyperplane face monoid if and only if it is in the quasivariety generated by the monoid obtained by adjoining an identity to the two-element left zero semigroup. We prove that this quasivariety is on the one hand polynomial time decidable, and on the other minimally non-finitely based. A similar result is obtained for the semigroups embeddable in complex hyperplane semigroups.
Cite
@article{arxiv.1212.6683,
title = {Semigroups embeddable in hyperplane face monoids},
author = {Stuart Margolis and Franco Saliola and Benjamin Steinberg},
journal= {arXiv preprint arXiv:1212.6683},
year = {2013}
}