A note on set-theoretic solutions of the Yang-Baxter equation

JOURNAL OF ALGEBRA

卷:500

Article; Proceedings Paper

Smoktunowicz, Agata¹ 

[1] Univ Edinburgh, Sch Math, James Clerk Maxwell Bldg,Kings Bldg, Edinburgh EH9 3FD, Midlothian, Scotland

关键词: Jacobson radical ring;    Braces;    Braided groups;    The Yang-Baxter equation;    Multipermutation solutions;   

DOI  :  10.1016/j.jalgebra.2016.04.015

来源: Elsevier

【 摘 要 】

This paper shows that every finite non-degenerate involutive set theoretic solution (X,r) of the Yang-Baxter equation whose permutation group g(X, r) has cardinality which is a cube-free number is a multipermutation solution. Some properties of finite braces are also investigated. It is also shown that if A is a left brace whose cardinality is an odd number and (-a) . b = -(a . b) for all a, b is an element of A, then A is a two-sided brace and hence a Jacobson radical ring. It is also observed that the semidirect product and the wreath product of braces of a finite multipermutation level is a brace of a finite multipermutation level. (C) 016 Elsevier Inc. All rights reserved.

【 授权许可】

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