287 citations · 1.4k across the 60 of their papers we have counts for
4 papers · 1 filter
On structure groups of set-theoretic solutions to the Yang-Baxter equation
V. Lebed, L. Vendramin
This paper explores the structure groups of finite non-degenerate set-theoretic solutions to the Yang-Baxter equation. Namely, we construct a finite quotient $\…
On skew braces (with an appendix by N. Byott and L. Vendramin)
A. Smoktunowicz, L. Vendramin
Braces are generalizations of radical rings, introduced by Rump to study involutive non-degenerate set-theoretical solutions of the Yang-Baxter equation (YBE). Skew braces were als…
PBW deformations of a Fomin-Kirillov algebra and other examples
I. Heckenberger, L. Vendramin
We begin the study of PBW deformations of graded algebras relevant to the theory of Hopf algebras. One of our examples is the Fomin-Kirillov algebra FK3. Another one appeared in a…
A characterization of finite multipermutation solutions of the Yang-Baxter equation
D. Bachiller, F. Cedó, L. Vendramin
We prove that a finite non-degenerate involutive set-theoretic solution (X,r) of the Yang-Baxter equation is a multipermutation solution if and only if its structure group G(X,r) a…