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Set-theoretic solutions to the Yang-Baxter equation and generalized semi-braces. (English) Zbl 1500.16036

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.

MSC:

16T25 Yang-Baxter equations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
16Y99 Generalizations
16N20 Jacobson radical, quasimultiplication
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