论文标题
Yang-baxter方程的左非分类理论解决方案和Q-Cycle集的动态扩展
Left non-degenerate set-theoretic solutions of the Yang-Baxter equation and dynamical extensions of q-cycle sets
论文作者
论文摘要
本文的第一个目的是在Yang-baxter方程的左非脱位生物设定理论溶液上提供足够的条件，以便它们是非分类的。特别是，我们将结果扩展到[36]中Rump获得的涉及解决方案，并以积极的方式回答Cedó，Jespers和Verwimp [19，问题4.2]提出的问题。此外，我们开发了Yang-Baxter方程的左非分类理论解决方案的扩展理论，该理论允许人们构建新的设定理论解决方案家族。
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 [36] and answer in a positive way to a question posed by Cedó, Jespers, and Verwimp [19, Question 4.2]. 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.
