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arXiv · 2207.02944

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

Přemysl Jedlička·Agata Pilitowska
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Abstract

We give a complete characterization of all indecomposable involutive solutions of the Yang-Baxter equation of multipermutation level~2. In the first step we present a construction of some family of such solutions and in the second step we prove that every indecomposable involutive solution of the Yang-Baxter equation with multipermutation level~2 is a homomorphic image of a solution previously constructed. Analyzing this epimorphism, we are able to obtain all such solutions up to isomorphism and enumerate these of small sizes.

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Přemysl Jedlička, Agata Pilitowska. 2022-07-06. Indecomposable involutive solutions of the Yang-Baxter equation of multipermutation level 2 with non-abelian permutation group. https://arxiv.org/abs/2207.02944

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