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

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• 作者：Dilian Yang¹ ; ^{dyang@uwindsor.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 16T25 ; 81R50 ; secondary ; 20F36 ; 18B40
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：1 April 2016
• 年：2016
• 卷：451
• 期：Complete
• 页码：494-525
• 全文大小：570 K

文摘

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.