Local derivations on finite-dimensional Lie algebras

Abstract

We prove that every local derivation on a finite-dimensional semisimple Lie algebra over an algebraically closed field of characteristic zero is a derivation. We also give examples of finite-dimensional nilpotent Lie algebras $\mathcal{L}$ with $\dim \mathcal{L}\ge 3$ which admit local derivations which are not derivations.

14 pages