This paper introduces Hopf braces, a new algebraic structure related to the Yang–Baxter equation, which include Rump’s braces and their non-commutative generalizations as particular cases. Several results of classical ...

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 and use this new structure to study not ...

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 also recently introduced as a tool to study ...

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 construct solutions of the parameter dependent ...

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 of skew left braces through strong left ...

Entrevista a Luis F. Leloir

We construct all skew braces of size pq (where p > q are primes) by using Byott’s classification of Hopf–Galois extensions of the same degree. For (Formula presented.) there exists only one skew brace which is the trivial ...

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 to study the unique product property in ...

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 left braces. Furthermore, we prove analogues ...