A. V. Antwerpen

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20182024

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math.RA2018

The structure monoid and algebra of a non-degenerate set-theoretic solution of the Yang-Baxter equation

Eric Jespers, Łukasz Kubat, Arne Van Antwerpen

For a finite involutive non-degenerate solution $(X, r)$ of the Yang--Baxter equation it is known that the structure monoid $M (X, r)$ is a monoid of I-type, and the structure algebra…

math.GR2018

Left semi-braces and solutions to the Yang-Baxter equation

Eric Jespers, Arne Van Antwerpen

Let $r : X^{2} \to X^{2}$ be a set-theoretic solution of the Yang-Baxter equation on a finite set $X$ . It was proven by Gateva-Ivanova and Van den Bergh that if $r$ is non-deg…