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 that 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.

中文翻译：

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Yang-Baxter方程和广义半括号的集合理论解

本文旨在介绍Yang-Baxter方程的集理论解的一种构建技术，称为强解半格。这项技术受半群的强半格的启发，可以使人们获得新的解决方案。特别地，该方法对于提供有限阶的非双射解是有用的。众所周知，大括号，斜大括号和半大括号与解决方案紧密相关。因此，我们基于这种新的解构造技术介绍了半括号的代数结构的一般化。