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arXiv · 1901.01471

The construction of multipermutation solutions of the Yang-Baxter equation of level 2

Přemysl Jedlička·Agata Pilitowska·Anna Zamojska-Dzienio
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Abstract

We study involutive set-theoretic solutions of the Yang-Baxter equation of multipermutation level 2. These solutions happen to fall into two classes -- distributive ones and non-distributive ones. The distributive ones can be effectively constructed using a set of abelian groups and a matrix of constants. Using this construction, we enumerate all distributive involutive solutions up to size 14. The non-distributive solutions can be also easily constructed, using a distributive solution and a permutation.

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Přemysl Jedlička, Agata Pilitowska, Anna Zamojska-Dzienio. 2019-01-05. The construction of multipermutation solutions of the Yang-Baxter equation of level 2. https://doi.org/10.1016/j.jcta.2020.105295

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