2-Local automorphisms on finite-dimensional Lie algebras

We prove that every 2-local automorphism on a finite-dimensional semi-simple Lie algebra LL over an algebraically closed field of characteristic zero is an automorphism. We also show that each finite-dimensional nilpotent Lie algebra LL with dim⁡L≥2dim⁡L≥2 admits a 2-local automorphism which is not an automorphism.