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arXiv · 1212.6683

Semigroups embeddable in hyperplane face monoids

Stuart Margolis·Franco Saliola·Benjamin Steinberg
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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.

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Stuart Margolis, Franco Saliola, Benjamin Steinberg. 2012-12-30. Semigroups embeddable in hyperplane face monoids. https://arxiv.org/abs/1212.6683

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