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math.QA2023
On the indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level
Marco Castelli
In this paper, we study the class of indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level, recently introduced by Cedó and Okniński in \cite{ce…
math.QA2023
On uniconnected solutions of the Yang-Baxter equation and Dehornoy's class
Marco Castelli, Santiago Ramírez
In the first part, we focus on indecomposable involutive solutions of the Yang-Baxter equation whose permutation group forces them to be uniconnected. Indecomposable involutive sol…
math.RA2023★ 1 cited
Studying solutions of the Yang-Baxter equation through skew braces, with an application to indecomposable involutive solutions with abelian permutation group
Marco Castelli, Senne Trappeniers
We connect properties of set-theoretic solutions to the Yang--Baxter equation to properties of their permutation skew brace. In particular, a variation of the multipermutation leve…