由线性函数构造的李代数与3-李代数的结构

摘要

It is concerned that the Lie algebra Vσ and 3-Lie algebra Vρσ which are constructed by a vector space V and its linear functions ρ,σ ∈ V*.And the Hom-Lie algebra structure of Vσ and the Hom3-Lie algebra structure of Vρσ are also studied.In the case of dimV =m ＜ ∞,structure of the derivation algebra Der(Vσ) is provided.%研究利用线性空间V上的线性函数ρ,σ构造李代数Vσ与3-李代数Vpσ,同时研究Vσ的Hom-李代数结构与Vpσ的Hom-3-李代数结构.对情形dimV=m＜∞,研究李代数Vσ的导子代数Der(Vσ)的结构.