齐次Rota-Baxter 3-李代数(Ⅰ)  

Homogeneous Rota-Baxter 3-Lie Algebras(Ⅰ)

作　　者：白瑞蒲[1] 亢闯闯 马越 侯帅 巴一[1] BAI Ruipu;KANG Chuangchuang;MA Yue;HOU Shuai;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,河北保定071002

出　　处：《河北大学学报（自然科学版）》2018年第1期1-6,共6页Journal of Hebei University(Natural Science Edition)

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

摘　　要：无限维单3-李代数Aω=∑m∈ZFLm上的齐性Rota-Baxter算子R是Aω的Rota-Baxter算子,且满足R(Lm)=f(m)Lm,其中f:Z→F.因为当λ不等于0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.因此,本文主要研究了Aω上权为1且满足|W1|<∞的齐性RotaBaxter算子的结构,并在3-李代数Aω的基底空间A上利用齐次Rota-Baxter算子构造了5类3-代数(A,[,,]j),并证明了3-李代数(A,[,,]j)都是齐性Rota-Baxter 3-李代数.Homogeneous Rota-Baxter operators R on the infinite dimensional simple 3-Lie Algebra Aω=∑m∈Z FL m are Rota-Baxter operators which satisfy R(L m)=f(m)L m,where f:Z→F is a function.Since Rota-Baxter operators of weightλwithλ≠0 on 3-Lie algebras are completely determined by the caseλ=1,the homogeneous Rota-Baxter operators of weight 1 on Aωwith|W 1|<∞are discussed.Five 3-Lie algebras(A,[,,]j)are constructed by the simple 3-Lie algebra Aωand its homogeneous Rota-Baxter operators.And it is proved that 3-Lie algebras(A,[,,]j)are all homogeneous Rota-Baxter 3-Lie algebras.

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

分 类 号：O152.5[理学—数学]