Semigroups of I-type
| dc.creator | Gateva-Ivanova, Tatiana | |
| dc.creator | Bergh, Michel Van den | |
| dc.date | 2003-08-08 | |
| dc.date.accessioned | 2026-07-07T05:00:14Z | |
| dc.date.available | 2026-07-07T05:00:14Z | |
| dc.description | Assume that $S$ is a semigroup generated by $\{x_1,...,x_n\}$, and let $\Uscr$ be the multiplicative free commutative semigroup generated by $\{u_1,...,u_n\}$. We say that $S$ is of \emph{$I$-typ}e if there is a bijection $v:\Uscr\r S$ such that for all $a\in\Uscr$, $\{v(u_1a),... v(u_na)\}=\{x_1v(a),...,x_nv(a)\}$. This condition appeared naturally in the work on Sklyanin algebras by John Tate and the second author. In this paper we show that the condition for a semigroup to be of $I$-type is related to various other mathematical notions found in the literature. In particular we show that semigroups of $I$-type appear in the study of the settheoretic solutions of the Yang-Baxter equation, in the theory of Bieberbach groups and in the study of certain skew binomial polynomial rings which were introduced by the first author. | |
| dc.identifier | https://arxiv.org/abs/math/0308071 | |
| dc.identifier | http://arxiv.org/abs/math/0308071 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68273 | |
| dc.subject | Quantum Algebra | |
| dc.title | Semigroups of I-type | |
| dc.type | text |