۲-local derivations on the perfect Lie algebras \mathfrak L^m

The notions of a ۲-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 ۲-local derivation. For a given Lie algebra \mathcal{L}, the main problem concerning these notions is to prove that every ۲-local derivation automatically becomes a derivation or to give examples of Lie algebras which admit ۲-local derivations which are not derivations. The present paper is devoted to study ۲-local derivations on the perfect Lie algebra \mathfrak L^m. We prove that every ۲-local derivation on this algebra is a derivation.

کلیدواژه ها:

Derivations ، Inner derivation ، Li algebras ، ۲-local derivations