Set-theoretic solutions to the Yang-Baxter equation and generalized semi-braces (Q2126316)

The authors introduce a new algebraic structure called generalized left semi-brace, that includes left semi-braces and is an instance of left semi-trusses. This structure provides set-theoretic solutions of the Yang-Baxter equation. Moreover, the authors introduce a construction technique that provides generalized left semi-braces, called the strong semilattice of generalized left semi-braces, and a construction technique for solutions called strong semilattice of solutions. Finally, they show that this method provides non-bijective solutions of finite order of the Yang-Baxter equation.