关于局部有限的DI-Lie代数的结构

ON THE STRUCTURE OF LOCALLY FINITE DI-LIE ALGEBRA

一个域F上的Lie代数L称为理想稠密分布的Lie代数,简称为DI-Lie代数。若对于L的任意子代数链A(?)B(?)C(这里A(?)B指的是A(?)B,且A≠B),则存在L的一个理想I使A(?)I(?)C。换句话说,在L的子代数格的任意开区间中,至少包含L的一个理想。本文给出并证明了局部有限的DI-Lie代数的结构定理。

An Lie algebra L over a field F is called Lie algebra with dense ideals,in short,DI-Lie algebra.If for any chain of subalgebra of L,ABC(where AB meansthat AB, but BC),there exists an ideal I of L such that AIC.In otherwords,in the lattice of subalgebras of L every open interval contains at least one idealof L.In this paper the structure theoremes of locally finite DI-Lie algebra arestated and proved.