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96 papers · 1 filter
Skew braces: a brief survey
Leandro Vendramin
Our primary focus is on the theory of skew braces, specifically exploring their connection with combinatorial solutions to the Yang-Baxter equation. Skew braces have recently emerg…
On two-sided skew braces
S. Trappeniers
In order to study two-sided skew braces, we introduce the notion of weakly trivial skew braces. We give a classification of such skew braces and show that they are essential in the…
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…
Algebraic constructions for Jacobi-Jordan algebras
A. L. Agore, G. Militaru
For a given Jacobi-Jordan algebra and a vector space over a field , a non-abelian cohomological type object is constructed: it classi…
Nilpotent Decomposition in Integral Group Rings
Eric Jespers, Wei-Liang Sun
A finite group is said to have the nilpotent decomposition property (ND) if for every nilpotent element of the integral group ring one has that also be…