Hom-李代数的广义Reynolds算子和Hom-NS-李代数  

Generalized Reynolds Operators on Hom-Lie Algebrasand Hom-NS-Lie Algebras

作　　者：徐森荣 汪为 赵嘉 XU Senrong;WANG Wei;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)》2025年第2期353-359,共7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,通过给定一个Hom-李代数及其表示,证明Hom-李代数上的强拟迹函数可以诱导3-Hom-李代数及其表示,从而证明Hom-李代数上的广义Reynolds算子也是诱导3-Hom-李代数上的广义Reynolds算子;其次,研究Hom-NS-李代数和广义Reynolds算子的相互导出性质,并给出相应范畴的伴随关系.Firstly,by providing a Hom-Lie algebra and its representation,we proved that a strong quasi-trace function on a Hom-Lie algebra could induce a 3-Hom-Lie al gebra and its representation,thereby proving that a generalized Reynolds operator on a Hom-Lie algebra was also a generalized Reynolds operator on the induced 3-Hom-Lie algebra.Secondly,we studied the mutual derivation properties of Hom-NS-Lie algebras and generalized Reynolds operators,and gave the adjoint relation of the corresponding categories.

关 键 词：Hom-李代数 广义Reynolds算子 3-Hom-李代数 Hom-NS-李代数 

分 类 号：O152.5[理学—数学]