Skew Braces and the Braid Equation on Sets

We discuss how skew braces allow us to construct solutions of the braid equation on the underlying set of a skew brace. First, we discuss methods introduced by W. Rump and then generalised by L. Guarnieri and L. Vendramin. Further, we present a recently introduced way of deforming solutions acquired from skew braces. We analyse skew braces of size 4. We linearise the deformed solutions and observe that the Jordan matrix of deformation is different to the original. That leads to the conclusion that deformations give us a tool to manipulate the solution not only up to the change of the basis.