The interplay between skew braces, the Yang–Baxter equation and Hopf–Galois structures

Abstract: In 2007, Wolfgang Rump introduced algebraic objects called braces, these gen- eralise Jacobson radical rings and are related to involutive non-degenerate set- theoretic solutions of the Yang–Baxter equation (YBE). These objects were subse- quently generalised to skew braces by Leandro Guarnieri and Leandro Vendramin in 2017, and a similar relation was shown to hold for non-degenerate set-theoretic solutions of the YBE which are not necessarily involutive. In this talk, we will de- scribe this interplay between skew braces and the YBE. We will also discuss their relation to Hopf–Galois structures and see how this extends the classical Galois theory in an elegant way.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar