一类非交换n-李代数的结构

吉林大学学报(理学版) ›› 2020, Vol. 58 ›› Issue (5): 1073-1078.

一类非交换n-李代数的结构

白瑞蒲, 吴婴丽

河北大学数学与信息科学学院, 河北保定 071002

收稿日期:2020-02-17 出版日期:2020-09-26 发布日期:2020-11-18
通讯作者: 白瑞蒲 E-mail:bairuipu@hbu.edu.cn

Structure of a Class of Non-Abelian n-Lie Algebras

BAI Ruipu, WU Yingli

College of Mathematics and Information Science, Hebei University, Baoding 071002, Hebei Province, China

Received:2020-02-17 Online:2020-09-26 Published:2020-11-18

摘要/Abstract

摘要： 研究满足β(L)=m-n+1的一类非交换n-李代数的结构, 对导代数维数小于4时的非交换n-李代数进行分类, 证明当导代数维数为1,2,3时分别存在2类、 6类、11类不同构的n-李代数, 进而证明满足β(L)=m-n+1, Z(L)L¹的非交换n-李代数具有性质(m-n+1)/2≤dimL¹≤m-n+1.

关键词: n-李代数, 极大Abel理想, 导代数

Abstract: We studied the structure of non-Abelian n-Lie algebras with β(L)=m-n+1, and classified n-Lie algebras that satisfied dim L¹<4. We prove that there are only 2,6 and 11 classes in the cases dimL¹=1,2,3, respectively. Furthermore, if β(L)=m-n+1 and Z(L)L¹, then (m-n+1)/2≤dimL¹≤m-n+1.

Key words: n-Lie algebra, maximal Abelian ideal, derived algebra

中图分类号:

O152.5

白瑞蒲, 吴婴丽. 一类非交换n-李代数的结构[J]. 吉林大学学报(理学版), 2020, 58(5): 1073-1078.

BAI Ruipu, WU Yingli. Structure of a Class of Non-Abelian n-Lie Algebras[J]. Journal of Jilin University Science Edition, 2020, 58(5): 1073-1078.