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.
Ilaria Colazzo
Lecturer in Pure Mathematics
My research interest focuses on studying algebraic structures associated with discrete versions of some equations in mathematical physics, such as the Yang-Baxter equation and the Pentagon equation. I am mainly interested in algebraic structures such as skew braces, trusses and generalisations that organise, classify and help to find solutions of the Yang-Baxter equation and the Pentagon equation with given properties.