有限维单李代数的2-局部导子

2-Local Derivations of Finite-Dimensional Simple Lie Algebras

设F是特征为零的代数封闭域,g为F上有限维单李代数.g上的一个映射φ称为2-局部导子,如果对任意的x,y∈g,存在导子D_(x,y):g→g,使φ(x)=D_(x,y)(x),φ(y)=D_(x,y)(y).本文证明g上的所有2-局部导子一定是内导子.

Let F be an algebraically closed field of characteristic 0,fl a finite-dimensional simple Lie algebra over F.A map y φ on g is called a 2-local derivation,if for any x,y ∈ g,there is a derivation Dx,y：g→g,such that φ（x） = Dx,y（x）,φ（y）=Dx,y（y）.We prove that any 2-local derivation of g is an inner derivation.