Set-theoretic solutions to the Yang-Baxter equation and generalized semi-braces

Abstract

This paper aims to introduce a construction technique of set-theoretic solutions of the Yang-Baxter equation, called strong semilattice of solutions. This technique, inspired by the strong semilattice of semigroups, allows one to obtain new solutions. In particular, this method turns out to be useful to provide non-bijective solutions of finite order. It is well-known braces, skew braces and semi-braces are closely linked with solutions. Hence, we introduce a generalization of the algebraic structure of semi-braces based on this new construction technique of solutions.

Cited by in corpus (10)

• Rota-Baxter operators on Clifford semigroups and the Yang-Baxter equation
• The Floquet Baxterisation
• Left non-degenerate set-theoretic solutions of the Yang-Baxter equation and semitrusses
• Set-theoretic solutions of the Yang-Baxter equation associated to weak braces
• Inverse semi-braces and the Yang-Baxter equation
• Extensions and automorphisms of Rota-Baxter groups
• Nilpotency in left semi-braces
• Solutions of the Yang-Baxter equation and strong semilattices of skew braces
• Reflections to set-theoretic solutions of the Yang-Baxter equation
• Deformed solutions of the Yang-Baxter equation associated to dual weak braces