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.
作者
白瑞蒲
亢闯闯
马越
侯帅
巴一
BAI Ruipu;KANG Chuangchuang;MA Yue;HOU Shuai;BA Yi(College of Mathematics and Information Science,Hebei University,Baoding 071002,China)
出处
《河北大学学报（自然科学版）》
CAS
北大核心
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)
