齐次Rota-Baxter 3-李代数(Ⅲ)  

Homogeneous Rota-Baxter 3-Lie algebras (Ⅲ)

作　　者：白瑞蒲[1] 侯帅 亢闯闯 马越 巴一[1] BAI Ruipu;HOU Shuai;KANG Chuangchuang;MA Yue;BA Yi(College of Mathematics and Information Science, Hebei University, Baoding 071002, China)

机构地区：[1]河北大学数学与信息科学学院,保定071002

出　　处：《黑龙江大学自然科学学报》2019年第2期157-163,共7页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金项目资助项目(11371245);河北省自然科学基金资助项目(A2014201006)

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 A ω=∑m∈Z 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.

关 键 词：3-李代数 齐次Rota-Baxter算子 齐次Rota-Baxter3-李代数 

分 类 号：O152.5[理学—数学]