摘要
设L是特征为零的代数封闭域F上的有限维单李代数.如果f:L→L为可逆映射,且满足[f(x),f(y)]=[x,y],对任意的x,y∈L,则称f是L上保强交换性的非线性可逆映射.证明L上保强交换性的可逆映射只能是恒等映射或负恒等映射.若映射δ:L→L满足[δ(x),y]+[x,δ(y)]=0,对任意的x,y∈L,则称δ为L上的非线性强积零导子.证明了单李代数L上非线性强积零导子只能是零映射.
Let L be a finite-dimensional simple Lie algebra over an algebrically closed field F of characteristic zero. A nonlinear mapf：L→L is called a strong commutativity preserving map iff is invertible and for anyx,y ∈ L, [f（x） ,f（y） ] = [x,y] . It shows that a strong commutativity preserving map over L is just an identical mapping or negative identical mapping. A nonlinear map δ ：L→ L is called a nonlinear strong product zero derivation if for anyx,y → L, [ δ（x）, y] ＋ [x,δ（y） ] = 0 . It is shown that a strong product zero derivation is just a zero map.
出处
《福建师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2013年第4期5-8,共4页
Journal of Fujian Normal University：Natural Science Edition
基金
国家自然科学基金资助项目(11101084)
关键词
单李代数
非线性映射
保强交换性
非线性强积零导子
simple Lie algebra
non-linear invertible map
strong commutativity preserving map
non-linear strong product zero derivation
