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Semigroups of I-type | | Tatiana Gateva-Ivanova
; Michel Van den Bergh
; | | Date: |
8 Aug 2003 | | Subject: | Quantum Algebra | math.QA | | Abstract: | 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 $v:UscrS$ such that for all $ainUscr$, ${v(u_1a),... v(u_na)}={x_1v(a),...,x_nv(a)}$. 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. | | Source: | arXiv, math.QA/0308071 | | Services: | Forum | Review | PDF | Favorites | |
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