N-Derivations for Finitely Generated Graded Lie Algebras

The N-derivation is a natural generalization of derivation and triple derivation. Let G be a finitely generated Lie algebra graded by a finite-dimensional Cartan subalgebra. In this paper, a sufficient condition for the Lie N-derivation algebra of G coinciding with the Lie derivation algebra of G is given. As applications, any N-derivation of the SchrodingerVirasoro algebra, generalized Witt algebra, Kac-Moody algebra or their Borel subalgebra is a derivation.