287 citations · 1.4k across the 60 of their papers we have counts for
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An explicit description of the second cohomology group of a quandle
Agustín García Iglesias, Leandro Vendramin
We use the inflation-restriction sequence and a result of Etingof and Graña on the rack cohomology to give a explicit description of 2-cocycles of finite indecomposable quandles wi…
Skew braces and the Yang-Baxter equation
L. Guarnieri, L. Vendramin
Braces were introduced by Rump to study non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation. We generalize Rump's braces to the non-commutative setting an…
Homology of left non-degenerate set-theoretic solutions to the Yang-Baxter equation
V. Lebed, L. Vendramin
This paper deals with left non-degenerate set-theoretic solutions to the Yang-Baxter equation (=LND solutions), a vast class of algebraic structures encompassing groups, racks, and…
Extensions of set-theoretic solutions of the Yang-Baxter equation and a conjecture of Gateva-Ivanova
L. Vendramin
We develop a theory of extensions for involutive and nondegenerate solutions of the set-theoretic Yang-Baxter equation and use it to produce new families of solutions. As an applic…