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http://hdl.handle.net/1942/3184
Title: | Semigroups of I-type | Authors: | Gateva-Ivanova, T VAN DEN BERGH, Michel |
Issue Date: | 1998 | Publisher: | ACADEMIC PRESS INC | Source: | JOURNAL OF ALGEBRA, 206(1). p. 97-112 | Abstract: | Assume that S is a semigroup generated by {x(1),..., x(n)}, and let U be the multiplicative free commutative semigroup generated by {u(1),..., u(n)}. We say that S is of I-type if there is a bijective upsilon : U --> S such that for all a is an element of U, {upsilon(u(1)a),..., upsilon(u(n)a)} = {x(1)upsilon(a),..., x(n)upsilon(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 set-theoretic 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. (C) 1998 Academic Press. | Notes: | Bulgarian Acad Sci, Inst Math, Sect Algebra, Sofia 113, Bulgaria. Limburgs Univ Centrum, Dept WNI, B-3590 Diepenbeek, Belgium.Gateva-Ivanova, T, Bulgarian Acad Sci, Inst Math, Sect Algebra, Sofia 113, Bulgaria. | Document URI: | http://hdl.handle.net/1942/3184 | ISI #: | 000075260600007 | Type: | Journal Contribution | Validations: | ecoom 1999 |
Appears in Collections: | Research publications |
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