2-local derivations on the perfect lie algebras $mathfrak l^m$

The notions of a 2-local derivation for lie algebras are defined similarly to the associative case. it is clear that every derivation of a lie algebra $mathcal{l}$ is a 2-local derivation. for a given lie algebra $mathcal{l}$, the main problem concerning these notions is to prove that every 2-local derivation automatically becomes a derivation or to give examples of lie algebras which admit 2-local derivations which are not derivations. the present paper is devoted to study 2-local derivations on the perfect lie algebra $mathfrak l^m$. we prove that every 2-local derivation on this algebra is a derivation.