齐次Rota-Baxter 3-李代数(Ⅲ)

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英文篇名：Homogeneous Rota-Baxter 3-Lie algebras (Ⅲ) 作者：白瑞蒲 ; 侯帅 ; 亢闯闯 ; 马越 ; 巴一 英文作者：BAI Ruipu;HOU Shuai;KANG Chuangchuang;MA Yue;BA Yi;College of Mathematics and Information Science, Hebei University; 关键词：3-李代数 ; 齐次Rota-Baxter算子 ; 齐次Rota-Baxter ; 3-李代数 英文关键词：3-Lie algebras;;homogeneous Rota-Baxter operators;;homogeneous Rota-Baxter 3-Lie algebras 中文刊名：HLDZ 英文刊名：Journal of Natural Science of Heilongjiang University 机构：河北大学数学与信息科学学院; 出版日期：2019-04-25 出版单位：黑龙江大学自然科学学报 年：2019 期：v.36 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) 语种：中文; 页：HLDZ201902004 页数：7 CN：02 ISSN：23-1181/N 分类号：35-41

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 ■ and homogeneous Rota-Baxter operators R(satisfying R(L_m)=f(m+k)L_(m+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.

引文

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