相对罗巴算子的拟迹函数方法和上同调  

Quasi-trace Function Method and Cohomology of Relative Rota-Baxter Operators

作　　者：徐森荣 谭易兰 赵嘉 XU Senrong;TAN Yilan;ZHAO Jia(School of Mathematical Sciences,Jiangsu University,Zhenjiang 212013,Jiangsu Province,China;School of Sciences,Nantong University,Nantong 226019,Jiangsu Province,China)

机构地区：[1]江苏大学数学科学学院,江苏镇江212013 [2]南通大学理学院,江苏南通226019

出　　处：《吉林大学学报（理学版）》2023年第6期1313-1318,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12201253);江苏省自然科学基金(批准号:BK20220510)。

摘　　要：首先,用拟迹函数方法给出低阶情形下李表示对的相对罗巴算子的上同调群到诱导3-李表示对的相对罗巴算子的上同调群的对应关系;其次,利用构造链映射方法,得到李表示对和诱导3-李表示对的相对罗巴算子的任意阶数大于等于2的上同调群之间的同态映射.Firstly,by using the method of quasi-trace functions,the corresponding relationship between the cohomology group of the relative Rota-Baxter operator of a Lie representation pair and the cohomology group of the relative Rota-Baxter operator of the induced 3-Lie representation pair in the low-order cases was given.Secondly,by using the method of constructing chain maps,the homomorphism between the cohomology groups of the relative Rota-Baxter operator of a Lie representation pair and the induced 3-Lie representation pair with any order greater than or equal to 2 was obtained.

关 键 词：相对罗巴算子 拟迹函数 上同调 李代数 3-李代数 

分 类 号：O152.5[理学—数学]