Simple solutions of the Yang-Baxter equation

Abstract

We present a characterization of simple finite non-degenerate bijective set-theoretic solutions of the Yang-Baxter equation in terms of the algebraic structure of the associated permutation skew left braces. In particular, we prove that they need to have a unique minimal non-zero ideal and modulo this ideal one obtains a trivial skew left brace of cyclic type.

Arne Van Antwerpen

Post-doctoral assistant in Mathematics

My research interests include set-theoretic solutions of the Yang-Baxter equation, skew left braces and quadratic algebras.