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…
Finiteness conditions on skew braces and solutions of the Yang-Baxter equation
Rosa Cascella, Silvia Properzi, Arne Van Antwerpen
A finite non-degenerate set-theoretic solution of the Yang-Baxter equation gives rise to a structure skew brace that is a -skew brace, i.e. every element has…
Bijective solutions to the Pentagon Equation
I. Colazzo, J. OkniÅski, 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…
On the cabling of non-involutive set-theoretic solutions of the Yang--Baxter equation
Ilaria Colazzo, Arne Van Antwerpen
We extend the cabling method by Lebed, RamÃrez and Vendramin from involutive to bijective non-degenerate set-theoretic solutions of the Yang--Baxter equation by working in the Yan…
Simple solutions of the Yang-Baxter equation
Ilaria Colazzo, Eric Jespers, Åukasz 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…