On Cardinalities whose Arithmetical Properties Determine the Structure of Solutions of the Yang--Baxter Equation

Abstract: We provide purely arithmetical characterisations of those natural numbers n for which every non-degenerate set-theoretic solution of cardinality n of the Yang--Baxter equation arising from a skew brace (sb-solution for short) satisfies some relevant properties, such as being a flip, involutive, or multipermutation. This is based on joint work with M. Ferrara and C. Tsang.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar