论文标题
Hom-Yang-Baxter方程和HOM-CYCLE集合的设置理论解决方案
Set-theoretical solutions to the Hom-Yang-Baxter equation and Hom-cycle sets
论文作者
论文摘要
通过相关的代数系统（例如循环集和括号）对杨巴克斯特方程的设定理论解决方案进行了广泛的研究，该系统也已开发出动态版本。没有工作重点是Hom-Yang-Baxter方程（简称Hybe）的设定理论解决方案。本文研究了Hybe和相关代数系统的设定理论解决方案，称为HOM-CYCLE集合。我们表征了左非分类涉及的集合理论解决方案和HOM-CYCLE集合，并建立了它们的关系。我们讨论了HOM循环集，周期集，左非分类涉及的设置理论解决方案和Yang-Baxter方程之间的连接。
Set-theoretic solutions to the Yang-Baxter equation have been studied extensively by means of related algebraic systems such as cycle sets and braces, dynamical versions of which have also been developed. No work focuses on set-theoretic solutions to the Hom-Yang-Baxter equation (HYBE for short). This paper investigates set-theoretic solutions to HYBE and associated algebraic system, called Hom-cycle sets. We characterize left non-degenerate involutive set-theoretic solutions to HYBE and Hom-cycle sets, and establish their relations. We discuss connections among Hom-cycle sets, cycle sets, left non-degenerate involutive set-theoretic solutions to HYBE and the Yang-Baxter equation.
