Indecomposable involutive solutions to the Yang-Baxter equation of size $p^2$

This talk is based on joint work with Carsten Dietzel and Senne Trappeniers. We study indecomposable involutive non-degenerate set-theoretic solutions to the Yang-Baxter equation. Building upon the works of Jedlička-Pilitowska and Cedó-Okniński and through the study of their associated permutation skew brace, we fully classify such solutions of prime-squared size.

May 6, 2024