A characterization of finite simple set-theoretic solutions of the Yang-Baxter equation. (English) Zbl 1536.16032
This paper is devoted to the characterization of finite simple involutive nondegenerate set-theoretic solutions of the Yang-Baxter equation by means of left braces (the algebraic structures introduced by
W. Rump [Adv. Math. 193, No. 1, 40–55 (2005; Zbl 1074.81036)]). This provides a family of left braces that give rise to simple set-theoretic solutions of the Yang-Baxter equation. The main result gives a characterization of simple solutions by means of left braces. As an application, the author presents some examples of simple solutions, some of which are different from the ones obtained previously in the literature.
Reviewer: Oleksandr Tsymbaliuk (West Lafayette)
MSC:
| 16T25 | Yang-Baxter equations |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
Citations:
Zbl 1074.81036Software:
YangBaxterReferences:
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