36 citations · 60 across the 5 of their papers we have counts for
5 papers
Free Skew Braces and Free Solutions of the Yang--Baxter Equation
Eric Jespers, Thomas Letourmy, Silvia Properzi +2
We offer a workable construction of the free right nilpotent skew braces of arbitrary class which allows us to prove (among many other things) that this free object has free additi…
Simple solutions of the Yang-Baxter equation
Ilaria Colazzo, Eric Jespers, Łukasz Kubat +1
We study simple set-theoretic solutions of the Yang-Baxter equation that are finite and non-degenerate. Such retractable solutions are fully described and to investigate the irretr…
On various types of nilpotency of the structure monoid and group of a set-theoretic solution of the Yang--Baxter equation
F. Cedó, E. Jespers, Ł. Kubat +2
Given a finite bijective non-degenerate set-theoretic solution of the Yang--Baxter equation we characterize when its structure monoid is Malcev nilpotent. Applying…
Radical and weight of skew braces and their applications to structure groups of solutions of the Yang-Baxter equation
E. Jespers, Ł. Kubat, A. Van Antwerpen +1
We define the radical and weight of a skew left brace and provide some basic properties of these notions. In particular, we obtain a Wedderburn type decomposition for Artinian skew…
Factorizations of skew braces
E. Jespers, Ł. Kubat, A. Van Antwerpen +1
We introduce strong left ideals of skew braces and prove that they produce non-trivial decomposition of set-theoretic solutions of the Yang-Baxter equation. We study factorization…