2-Local automorphisms of finite-dimensional simple Lie algebras

Let F be an algebraically closed field of characteristic 0, L be a finite-dimensional simple Lie algebra of type Al (l≥1), Dl (l≥4), Ek (k=6,7,8) over F. A not necessarily linear map φ:L→L is called a 2-local automorphism if for every x,y∈L there is an automorphism φx,y:L→L, depending on x and y, such that φ(x)=φx,y(x), φ(y)=φx,y(y). In this paper, we prove that any 2-local automorphism of L is an automorphism.