Simplicity of indecomposable set-theoretic solutions of the Yang-Baxter equation

被引：4

作者：

Castelli, Marco ^{[1
]}

Mazzotta, Marzia ^{[1
]}

Stefanelli, Paola ^{[1
]}

机构：

[1] Univ Salento, Dipartimento Matemat & Fis Ennio De Giorgi, Via Prov Lecce Arnesano, I-73100 Lecce, Italy

来源：

FORUM MATHEMATICUM | 2022年 / 34卷 / 02期

关键词：

Set-theoretic solution; Yang-Baxter equation; cycle set; dynamical extension;

D O I：

10.1515/forum-2021-0189

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper aims to deepen the theory of bijective non-degenerate set-theoretic solutions of the Yang-Baxter equation, not necessarily involutive, by means of q-cycle sets. We entirely focus on the finite indecomposable ones, among which we especially study the class of simple solutions. In particular, we provide a group-theoretic characterization of these solutions, including their permutation groups. Finally, we deal with some open questions.

引用

页码：531 / 546

页数：16

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