齐次Rota-Baxter 3-李代数(Ⅲ)

摘要

We study the structure of 3-Lie algebras constructed by the infinite dimensional simple 3-Lie algebra Aω=∑m∈Ζ?FLm and homogeneous Rota-Baxter operators R (satisfying R (Lm) =f (m+k) Lm+k, where f:Z→F) with non-zero weight. Since Rota-Baxter operators of weight λ with λ≠0 are determined by the case λ=1, the concrete expression of homogeneous Rota-Baxter operators of weight 1 which satisfy f (0) +f (1) +1≠0 are provided. And sixteen homogeneous Rota-Baxter 3-Lie algebras of weight 1 are constructed.%研究了由无限维单3-李代数Aω=∑m∈ΖFLm和Aω上具有非零权的齐次Rota-Baxter算子R (满足R (Lm) =f (m+k) Lm+k, 其中f:Z→F) 所构造的3-李代数的结构.当权入不等于零时, 3-李代数的权为λ的Rota-Baxter算子完全由权为1的Rota-Baxter算子所决定, 给出Aω上权为1且满足f (0) +f (1) +1≠0的齐次Rota-Baxter算子的具体表达式, 利用齐次Rota-Baxter算子, 构造16类权为1的齐次Rota-Baxter3-李代数.