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 A(l) (l >= 1), D-l (l >= 4), E-k (k = 6, 7, 8) over F. A not necessarily linear map phi : L -> L is called a 2-local automorphism if for every x,y is an element of L there is an automorphism phi(x,y) : L -> L, depending on x and y, such that phi(x) = phi(x,y)(x), phi(y) = phi(x,y)(y). In this paper, we prove that any 2-local automorphism of L is an automorphism. (C) 2015 Elsevier Inc. All rights reserved.