摘要
本文对子空间均为子代数的李代数，称为Ｓ．Ａ－李代数，进行了讨论。得到的主要结果为：Ｓ．Ａ－李代数Ｌ的结构为：Ｌ＝Ｈｊ，其中Ｈｉ＝｛ｘ∈Ｌ｜ｘ为Ｈｊ的ａｄ－幕零元｝；Ｌ的李来运算为：［ｘ，ｙ］＝２ｘ。ａ∈Ｆ。ｘ∈Ｈｉ，ｙ∈Ｈｊ，ｉ＜ｊｉ，ｊ＝１…，Ｓ。［ｘ．ｙ］＝０．ｘ，ｙ∈Ｈｉｉ＝１，…Ｓ。
In this paper,we discuss a class of Lie algebras,its subspaces are all the lie subalgebras This Lie algebra is called S.A-Lie algebra.We obtain the following main result:Assume L is a finite dimenssional Lie algebra over a field F of characteristic 0.Then L is a S.A -Lie algebra if and only if (Space direct sum)where H,={x∈L|ad,s1x is nilpotent.}(Si=Hj)and its Lie products are [x,y]=0 x,y∈Hi(i=1,2,…,r)[x,y] =ax,xi∈Hi,,y∈Hj,i<j (i,j= 1,2,…,r),a∈F.
出处
《哈尔滨师范大学自然科学学报》
1996年第1期19-23,共5页
Natural Science Journal of Harbin Normal University
