In 2007, Wolfgang Rump introduced algebraic objects called braces, these generalize Jacobson radical rings and are related to involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation (YBE). These objects were subsequently generalized 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 describe 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.
This video is part of the European Non-Associative Algebra Seminar series.
