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
程紫莹 1吕家凤 1亢闯闯1
作者信息
- 1. 浙江师范大学 数学科学学院,浙江 金华 321004
- 折叠
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.
Abstract
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 representa-tions 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Key words
3-Pre-Lie algebras/(O)-operators/3-Lie algebras/Pre-Lie algebras引用本文复制引用
出版年
2025
NETL
NSTL
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