Local Automorphisms on Finite-Dimensional Lie and Leibniz Algebras

We prove that a linear mapping on the algebra sl(n) of all trace zero complex matrices is a local automorphism if and only if it is an automorphism or an antiautomorphism. We also show that a linear mapping on a simple Leibniz algebra of the form sl(n)+-J , is a local automorphism if and only if it is an automorphism. We give examples of finite-dimensional nilpotent Lie algebras I with dim I >= 3 which admit local automorphisms which are not automorphisms.