The interplay between k-graphs and the Yang-Baxter equation

JOURNAL OF ALGEBRA

卷:451

Article

Yang, Dilian¹ 

[1] Univ Windsor, Dept Math & Stat, Windsor, ON N9B 3P4, Canada

关键词: Yang-Baxter equation;    k-Graph;    Set-theoretic solution;   

DOI  :  10.1016/j.jalgebra.2016.01.001

来源: Elsevier

【 摘 要 】

In this paper, we initiate the study of the interplay between k-graphs and the Yang Baxter equation. For this, we provide two very different perspectives. On one hand, we show that the set of all set-theoretic solutions of the Yang Baxter equation is a special class of single-vertex k-graphs. As a consequence, we construct an infinite family of large solutions of the Yang Baxter equation from an arbitrarily given one. On the other hand, we prove that all single-vertex k-graphs are YB-semigroups of square-free, involutive solutions of the Yang Baxter equation. Other various connections are also investigated. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free