Semigroups embeddable in hyperplane face monoids

Stuart Margolis, Franco Saliola, Benjamin Steinberg
<span title="2013-11-27">2013</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="" style="color: black;">Semigroup Forum</a> </i> &nbsp;
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.
more &raquo; ... similar result is obtained for the semigroups embeddable in complex hyperplane semigroups.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1007/s00233-013-9542-3</a> <a target="_blank" rel="external noopener" href="">fatcat:5dzo25vulvbynhqlwdd6l7jdcm</a> </span>
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