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.
| Original language | English |
|---|---|
| Pages (from-to) | 236-248 |
| Number of pages | 13 |
| Journal | Semigroup Forum |
| Volume | 89 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Aug 2014 |
Bibliographical note
Publisher Copyright:© 2013, Springer Science+Business Media New York.
Funding
The second author was supported in part by NSERC and FRQNT. The third author was supported in part by the Simon’s Foundation collaboration grant 245268. The first and third author’s research was supported by Grant No. 2012080 from the United States-Israel Binational Science Foundation (BSF).
| Funders | Funder number |
|---|---|
| Simon’s Foundation | 2012080, 245268 |
| Natural Sciences and Engineering Research Council of Canada | |
| United States-Israel Binational Science Foundation | |
| Fonds de recherche du Québec – Nature et technologies |
Keywords
- Hyperplane arrangements
- Left regular bands
- Quasivarieties