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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.GR2026
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…
math.GR2026
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…