无穷维3-李代数的可列结构  

The split structure of an infinite dimensional 3-Lie-algebras

作　　者：周檬[1] 潘学功[1] 白喜梅 ZHOU Meng;PAN Xue-gong;BAI Xi-mei(Department of Software Technology,Heibei Software Institute,Baoding 071000,China;Department of Mathematics,Hebei University,Baoding 071002,China)

机构地区：[1]河北软件职业技术学院软件技术系,河北保定071000 [2]河北大学数学系,河北保定071002

出　　处：《东北师大学报（自然科学版）》2022年第1期6-8,共3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：研究了实数域上一类可微的三元函数构成的无限维单3-李代数L;的可列结构.证明了3-李代数L;的可列Cartan子代数是彼此同构的2维交换子代数,给出了L;关于任意一个可列Cartan子代数的根系Λ、根空间分解及根子空间,并对根系及根空间的结构进行了研究.The split structure of an infinite dimensional 3-Lie-algebra L;,which is constructed by a class of 3 variables differentiable functions, is discussed.It is proved that the split Cartan subalgebras are isomorphic 2-dimensional abelian subalgebras.The root subspaces decomposition, root system, root subspaces of L;associative to a split Cartan subalgebra H;are provided, and structures of root system and root subspaces are studied.

关 键 词：3-李代数 可列Cartan子代数 根系 

分 类 号：O152.5[理学—数学]