287 citations · 1.4k across the 60 of their papers we have counts for
11 papers · 1 filter
The Köthe conjecture via point modules
B. Greenfeld, B. King, L. Vendramin
We give a short construction refuting the Köthe Conjecture. The construction is based on the point module approach to the problem, introduced by the first-named and second-named au…
On Noetherian pointed Hopf algebras
N. Andruskiewitsch, I. Heckenberger, L. Vendramin
In arXiv:1405.4105 it was asked whether an affine Hopf algebra with finite Gelfand-Kirillov dimension is necessarily Noetherian. It is well-known that the converse is not true --ta…
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…
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,…
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…
Factorizations of skew braces
E. Jespers, Ł. Kubat, A. Van Antwerpen +1
We introduce strong left ideals of skew braces and prove that they produce non-trivial decomposition of set-theoretic solutions of the Yang-Baxter equation. We study factorization…
Retractability of solutions to the Yang-Baxter equation and -nilpotency of skew braces
E. Acri, R. Lutowski, L. Vendramin
Using Bieberbach groups we study multipermutation involutive solutions to the Yang-Baxter equation. We use a linear representation of the structure group of an involutive solution…
Combinatorial solutions to the reflection equation
Agata Smoktunowicz, Leandro Vendramin, Robert Weston
We use ring-theoretic methods and methods from the theory of skew braces to produce set-theoretic solutions to the reflection equation. We also use set-theoretic solutions to const…
Problems on skew left braces
Leandro Vendramin
Braces were introduced by Rump as a generalization of Jacobson radical rings. It turns out that braces allow us to use ring-theoretic and group-theoretic methods for studying invol…
Skew left braces of nilpotent type
Ferran Cedo, Agata Smoktunowicz, Leandro Vendramin
We study series of left ideals of skew left braces that are analogs of upper central series of groups. These concepts allow us to define left and right nilpotent skew left braces.…
On skew braces and their ideals (with an Appendix by Agata Smoktunowicz)
A. Konovalov, A. Smoktunowicz, L. Vendramin
We define combinatorial representations of finite skew braces and use this idea to produce a database of skew braces of small size. This database is then used to explore different…