Płonka sums of set-theoretical solutions of the Yang-Baxter equation

Abstract: The Płonka sum is one of the most significant composition methods in Universal Algebra introduced by Jerzy Płonka in 1967. In particular, Clifford semigroups have turned out to be the first instances of Płonka sums of groups. In this talk, we illustrate a method for constructing set-theoretical solutions of the Yang-Baxter equation that is inspired by the notion of the Płonka sums. Moreover, we will show how to obtain solutions of this type by considering dual weak braces, algebraic structures recently studied and described in a joint work with Francesco Catino and Marzia Mazzotta.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar