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arXiv · 1506.03117

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

Dilian Yang
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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. One 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.

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Dilian Yang. 2015-06-09. The interplay between $k$-graphs and the Yang-Baxter equation. https://arxiv.org/abs/1506.03117

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