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

@article{Catino2020SettheoreticST,
  title={Set-theoretic solutions to the Yang–Baxter equation and generalized semi-braces},
  author={Francesco Catino and Ilaria Colazzo and Paola Stefanelli},
  journal={Forum Mathematicum},
  year={2020},
  volume={33},
  pages={757 - 772}
}
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 that braces, skew braces and semi-braces are closely linked with solutions. Hence, we introduce a generalization of the… Expand
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