Article ID Journal Published Year Pages File Type
4583937 Journal of Algebra 2016 32 Pages PDF
Abstract

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.

Keywords
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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