摘要
研究了由无限维单3-李代数■和A_ω上具有非零权的齐次Rota-Baxter算子R(满足R(L_m)=f(m+k)L_(m+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A_ω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。
We study the structure of 3-Lie algebras constructed by the infinite dimensional simple 3-Lie algebra ■ and homogeneous Rota-Baxter operators R(satisfying R(L_m)=f(m+k)L_(m+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.
引文
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