三维单左对称代数上的Nijenhuis算子和经典Yang-Baxter方程解  

Nijenhuis operators on three-dimensional simple left symmetric algebras and solutions of classical Yang-Baxter equation

作　　者：高翔[1] 吕家凤[1] 亢闯闯 GAO Xiang;LYU Jiafeng;KANG Chuangchuang(School of Mathematical Sciences,Zhejiang Normal University,Jinhua 321004,China)

机构地区：[1]浙江师范大学数学科学学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2024年第3期275-280,共6页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金面上资助项目(12071441)。

摘　　要：为了研究三维复单左对称代数上的Nijenhuis算子,通过求解结构常数构成的二次方程组,对三维复单左对称代数上的Nijenhuis算子进行了刻画.此外,利用所得结果,给出了半直积邻接李代数上的经典Yang-Baxter方程的解.It was aimed to study Nijenhuis operators on 3-dimensional complex simple left symmetric algebras,by solving quadratic equations composed of structural constants,Nijenhuis operators on 3-dimensional complex simple left symmetric algebras were described.The solutions of classical Yang-Baxter equation on the semi-direct product sub-adjacent Lie algebras were then obtained by using the presented results.

关 键 词：Nijenhuis算子 左对称代数 邻接李代数 经典Yang-Baxter方程 

分 类 号：O153[理学—数学]