Set-theoretic solutions of the Yang--Baxter equation and di-skew braces.

Abstract: The aim of this talk is to provide a brief overview of the role of generalised digroups in the study of the set-theoretic Yang-Baxter equation (YBE). Digroups are algebraic objects endowed with two binary associative operations that arose in the investigations of R. Felipe, K. Liu and M. Kinyon around the so-called coquecigrue problem, as first stated by J. L. Loday. In detail, we will introduce the structure of di-skew braces as a split notion of usual skew braces and show how they provide a class of non-degenerate solutions to the set-theoretic YBE whose (left) derived rack is not necessarily idempotent. Moreover, we will describe basic properties of such solutions through the lens of self-distributivity and explore related ideas. Based on a joint work with Paola Stefanelli.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar