24 citations · 58 across the 9 of their papers we have counts for
11 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…
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…
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…
Common divisor graphs for skew braces
Silvia Properzi, Arne Van Antwerpen
We introduce two common divisor graphs associated with a finite skew brace, based on its - and -orbits. We prove that the number of connected components is at most two and th…
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…
Coleman automorphisms of finite groups and their minimal normal subgroups
Arne Van Antwerpen
In this paper, we show that all Coleman automorphisms of a finite group with self-central minimal non-trivial characteristic subgroup are inner; therefore the normalizer property h…