3 papers
math.GR2026
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…
math.GR2024
Bijective solutions to the Pentagon Equation
I. Colazzo, J. Okniński, A. Van Antwerpen
A complete classification of all finite bijective set-theoretic solutions to the Pentagon Equation is obtained. First, it is shown that every such solution determines a sem…
math.RA2023
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…