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Iterated matched products of finite braces and simplicity; new solutions of the Yang-Baxter equation
D. Bachiller, F. Cedó, E. Jespers +1
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 …
Extensions, matched products, and simple braces
David Bachiller
We show how to construct all the extensions of left braces by ideals with trivial structure. This is useful to find new examples of left braces. But, to do so, we must know the bas…
A family of irretractable square-free solutions of the Yang-Baxter equation
David Bachiller, Ferran Cedo, Eric Jespers +1
A new family of non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation is constructed. All these solutions are strong twisted unions of multipermutation solu…
Counterexample to a conjecture about braces
David Bachiller
We find an example of a finite solvable group (in fact, a finite -group) without any left brace structure (equiv. which is not an IYB group). Our argument is an improvement of a…
Solutions of the Yang-Baxter equation associated with a left brace
David Bachiller, Ferran Cedo, Eric Jespers
Given a left brace , a method to construct all the involutive, non-degenerate set-theoretic solutions of the YBE, such that is given. This meth…
Classification of braces of order
David Bachiller
A classification up to isomorphism of all left braces of order , where is any prime number, is given. To this end, we first classify all the left braces of order and $…