2-Local derivations on finite-dimensional Lie algebras

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