Let g be a finite dimensional simple Lie algebra over an
algebraically closed field K of characteristic 0. A linear map
φ:g→g is called a local automorphism if for
every x in g there is an automorphism φx of
g such that φ(x)=φx(x). We prove that a linear map
φ:g→g is local automorphism if and only if
it is an automorphism or an anti-automorphism.Comment: 14 page