A first aim of this paper is to give sufficient conditions on left non-degenerate bijective set-theoretic solutions of the Yang–Baxter equation so that they are non-degenerate. In particular, we extend the results on involutive solutions obtained by Rump in A decomposition theorem for square-free unitary solutions of the quantum Yang–Baxter equation, Adv. Math. 193 (2005) 40–55, https://doi.org/10.1016/j.aim.2004.03.019 and answer positively a question posed by Cedó et al. in Question 4.2 in Structure monoids of set-theoretic solutions of the Yang–Baxter equation, preprint (2019), https://arxiv.org/abs/1912.09710. Moreover, we develop a theory of extensions for left non-degenerate set-theoretic solutions of the Yang–Baxter equation that allows one to construct new families of set-theoretic solutions.

本文的第一个目的是给出关于 Yang-Baxter 方程的左非退化双射集理论解的充分条件，使得它们是非退化的。特别是，我们扩展了 Rump 在 A 分解定理中获得的对合解的结果，用于量子 Yang-Baxter 方程的无平方酉解，Adv。数学。 193 (2005) 40–55, https://doi.org/10.1016/j.aim.2004.03.019 并积极回答 Cedó等人提出的问题。在问题 4.2 中 Yang-Baxter 方程的集合论解的结构幺半群中，预印本 (2019)，https://arxiv.org/abs/1912.09710。此外，我们为 Yang-Baxter 方程的左非退化集合论解开发了一种扩展理论，该理论允许人们构建新的集合论解族。