一类4维3-李代数上的O-算子及导出的3-Pre-李代数  

O-operators on a type of 4-dimensional 3-Lie algebra and 3-Pre-Lie algebras

作　　者：程紫莹 吕家凤[1] 亢闯闯 CHENG Ziying;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）》2025年第1期21-29,共9页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学面上基金资助项目(12171206)。

摘　　要：李代数的Operad理论应用于3-李代数,可自然地构造出3-Pre-李代数,其与Pre-李代数有很多相似的性质.利用4维复3-李代数的分类以及3-李代数和O-算子的结构常数的关系,使用Maple软件求解三次非线性方程组,对一类4维复3-李代数上与伴随表示相结合的O-算子进行了刻画.此外,利用所得结果,给出了这些O-算子导出的26个3-Pre-李代数的例子.The Operad theory of Lie algebras was applied to 3-Lie algebras,leading to the construction of 3-Pre-Lie algebras,which shared many similar properties with Pre-Lie algebras.The cubic nonlinear equations were studied by using Maple software based on the classification of 4-dimensional complex 3-Lie algebras and their relationship with structure constants of O-operators.The O-operators associated with adjoint representations on a type of 4-dimensional complex 3-Lie algebras were investigated.In addition,based on the obtained results,26 examples of 3-Pre-Lie algebras derived from these O-operators were presented.

关 键 词：3-Pre-李代数 O-算子 3-李代数 Pre-李代数 

分 类 号：O153[理学—数学]