24 citations · 58 across the 9 of their papers we have counts for
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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…
Structure algebras of finite set-theoretic solutions of the Yang--Baxter equation
Ilaria Colazzo, Eric Jespers, Łukasz Kubat +1
Quadratic algebras related to some classes of finite left non-degenerate solutions (X,r) of the Yang--Baxter equation have been intensively studied since they are the associative r…
Finite idempotent set-theoretic solutions of the Yang--Baxter equation
Ilaria Colazzo, Eric Jespers, Łukasz Kubat +2
It is proven that finite idempotent left non-degenerate set-theoretic solutions of the Yang-Baxter equation on a set are determined by a left simple semigroup structure…
Nilpotency of skew braces and multipermutation solutions of the Yang-Baxter equation
E. Jespers, A. Van Antwerpen, L. Vendramin
We study relations between different notions of nilpotency in the context of skew braces and applications to the structure of solutions to the Yang-Baxter equation. In particular,…
Left non-degenerate set-theoretic solutions of the Yang-Baxter equation and semitrusses
Ilaria Colazzo, Eric Jespers, Arne Van Antwerpen +1
To determine and analyze arbitrary left non-degenerate set-theoretic solutions of the Yang-Baxter equation (not necessarily bijective), we introduce an associative algebraic struct…
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…