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arXiv · 2011.00229

Indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level 2 with abelian permutation group

Přemysl Jedlička·Agata Pilitowska·Anna Zamojska-Dzienio
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Abstract

We present a construction of all finite indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level at most 2 with abelian permutation group. As a consequence, we obtain a formula for the number of such solutions with a fixed number of elements. We also describe some properties of the automorphism groups in this case - in particular, we show they are regular abelian groups.

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Přemysl Jedlička, Agata Pilitowska, Anna Zamojska-Dzienio. 2020-10-31. Indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level 2 with abelian permutation group. https://doi.org/10.1515/forum-2021-0130

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