The construction of multipermutation solutions of the Yang-Baxter equation of level 2
arXiv:1901.01471 · doi:10.1016/j.jcta.2020.105295
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.
arXiv comment25 pages; Section 6 modified and Section 9 deleted - now we focus only on the construction
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