In an attempt to understand the origins and the nature of the law binding two group
operations together into a skew brace, introduced by Guarnieri and Vendramin as a non …

Left Braces: Solutions of the Yang-Baxter Equation * 1 Introduction Page 1 Advances in Group
Theory and Applications c 2018 AGTA - www.advgrouptheory.com/journal 5 (2018), pp. 33–90 …

In this paper we obtain new solutions of the Yang–Baxter equation that are left non-
degenerate through left semi-braces, a generalization of braces introduced by Rump. In …

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 involutive …

We study involutive non-degenerate set-theoretic solutions (X, r) of the Yang-Baxter
equation on a finite set X. The emphasis is on the case where (X, r) is indecomposable, so …

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 …

Braces were introduced by Rump as a promising tool in the study of the set-theoretic
solutions of the Yang-Baxter equation. It has been recently proved that, given a left brace $ B …

Using the theory of cycle sets and braces, non-degenerate indecomposable involutive set-
theoretic solutions to the Yang–Baxter equation are classified in terms of their universal …

The second cohomology group of a left skew brace with coefficients in a trivial left brace with
non-trivial actions is defined, its connection with extensions of a left skew brace by a trivial …

We develop a method to construct all the indecomposable involutive non-degenerate set-
theoretic solutions of the Yang-Baxter equation with a prime-power number of elements and …