Hom-3-Lie代数上的积结构和复结构  

Product and Complex Structures on Hom-3-Lie Algebras

作　　者：秦宇帆 林洁[2] 姜敬敬[3] QIN Yufan;LIN Jie;JIANG Jingjing(School of Science,Xinjiang Institute of Technology,Aksu Xinjiang 843100,China;Sino-European Institute of Aviation Engineering,Civil Aviation University of China,Tianjin 300300,China;School of Science,Civil Aviation University of China,Tianjin 300300,China)

机构地区：[1]新疆理工学院理学院,新疆阿克苏843100 [2]中国民航大学中欧航空工程师学院,天津300300 [3]中国民航大学理学院,天津300300

出　　处：《海南热带海洋学院学报》2023年第2期101-108,共8页Journal of Hainan Tropical Ocean University

基　　金：国家自然科学基金青年科学基金项目(12201624)。

摘　　要：为了研究Hom-3-Lie代数上的积结构和复结构,利用类似于研究3-Lie代数的方法及相关Lie代数理论,给出了Hom-3-Lie代数上的积结构和复结构存在的充要条件,得到了4类特殊的积结构和复结构,并在积结构和复结构间加了一个相容性条件,从而引进了Hom-3-Lie代数上的复积结构。In order to study the product and complex structure on Hom-3-Lie algebras,by using a method similar to the study of 3-Lie algebras and related Lie algebra theory,the sufficient conditions for the existence of product structures and complex structures on Hom-3-Lie algebras were given,four special product structures and complex structures were obtained,and a compatibility condition was added between the product structure and the complex structure,thus introducing the complex product structure on the Hom-3-Lie algebra.

关 键 词：Hom-3-Lie代数 Hom-Nijenhuis算子 积结构 复结构 复积结构 

分 类 号：O152.5[理学—数学]