具有B(L)=m-3的m维非交换3-李代数的结构  

The structure of m dimensional non-abelian n-Lie algebras withβ(L)=m-3

作　　者：白瑞蒲[1,2] 吴婴丽 BAI Rui-pu;WU Ying-li(College of Mathematics and Information Science,Hebei University,Baoding 071002,China;Key Laboratory 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：《东北师大学报（自然科学版）》2021年第4期6-10,共5页Journal of Northeast Normal University(Natural Science Edition)

基　　金：河北省自然科学基金资助项目(20182011126).

摘　　要：研究了满足β(L)=m-3的m维非交换3-李代数的结构,证明了β(L)=m-n的一般m维非交换n-李代数L幂零的充要条件,并分别对导代数维数是1和2且导代数包含中心的m维非交换3-李代数L的结构进行了刻画.The structure of m dimensional non-abelian 3-Lie algebras withβ(L)=m-3 is discussed.It is proved that an m dimensional non-abelian n-Lie algebra L withβ(L)=m-n is nilpotent if and only if it contains a nilpotent subalgebra A with L 1=A 1;and there exists an(m-n)dimensional abelian ideal I such that the complementary space of I has non-zero products.And then the structure of non-abelian m dimensional 3-Lie algebras L with one or two dimensional derived algebras satisfying Z(L)■L^(1) is characterized.

关 键 词：3-李代数 极大Abel理想 导代数 中心 

分 类 号：O152.5[理学—数学]