无限维齐性Rota-Baxter 3-李代数(Ⅱ)  

Infinite dimensional homogenous Rota-Baxter 3-Lie algebras(Ⅱ)

作　　者：白瑞蒲[1] 刘山[1] BAI Ruipu;LIU Shan(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,河北保定071002

出　　处：《河北大学学报（自然科学版）》2022年第4期343-349,共7页Journal of Hebei University(Natural Science Edition)

基　　金：河北省自然科学基金资助项目(20182011126)。

摘　　要：利用无限维单3-李代数A_(ω)上权为1且满足g(0)+g(1)+1=0的齐性Rota-Baxter算子R_(k),构造了13类齐性Rota-Baxter 3-李代数A_(k),1≤k≤13,证明了在齐性Rota-Baxter 3-李代数A_(k)中存在5类两两不同构的齐性Rota-Baxter 3-李代数D_(i),并研究了每一类3-李代数D_(i)的结构,1≤i≤5.13 classes of homogeneous Rota-Baxter 3-Lie algebras A_(k) are constructed by using the homogeneous Rota-Baxter operators R_(k),1≤k≤13,with weight 1 and satisfying g(0)+g(1)+1=0 on infinite dimensional simple 3-Lie algebra A_(ω).It is proved that there are 5 classes of non-isomorphic homogeneous Rota-Baxter 3-Lie algebras D_(i),1≤i≤5,in the homogeneous Rota-Baxter 3-Lie Algebra A_(k),1≤k≤13,and the structure of each class of 3-Lie algebras D_(i),1≤i≤5,is studied.

关 键 词：3-李代数 Rota-Baxter算子 齐性Rota-Baxter 3-李代数 

分 类 号：O152.5[理学—数学]