无限维齐性Rota-Baxter 3-李代数(Ⅰ)  

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

作　　者：白瑞蒲[1,2] 刘山 BAI Ruipu;LIU Shan(College of Mathematics and Information Science,Hebei University,Baoding 071002,China;KeyLaboratory of Machine Learning and Computational Intelligence of Hebei Province,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 [2]河北省机器学习与智能计算重点实验室,河北保定071002

出　　处：《河北大学学报（自然科学版）》2021年第6期633-637,共5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3-李代数A_(ω)={L_(m)|m∈Z}上所有满足h(0)+h(1)+1≠0的齐性Rota-Baxter算子R,构造了齐性Rota-Baxter 3-李代数,其中h:Z→F,R(L_(m))=h(m)L_(m),■_(m)∈Z,并对所构造的3-李代数进行了分类,证明了存在5类不同构的齐性Rota-Baxter 3-李代数Ck,1≤k≤5.By homogenous Rota-Baxter operators R satisfying h(0)+h(1)+1≠0 on the infinite dimensional 3-Lie algebra A_(ω)={L_(m)|m∈Z},homogenous Rota-Baxter 3-Lie algebras are constructed and the classification is given,where h:Z→F,R(L_(m))=h(m)L_(m),■_(m)∈Z.It is proved that there exist 5 classes homogenous Rota-Baxter 3-Lie algebras Ck,1≤k≤5.

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

分 类 号：O152.5[理学—数学]