Author(s): Cui Chen, Haifeng Lian
N-derivation is the natural generalization of derivation and triple deriva-tion. Let L be a finitely generated Lie algebra graded by a finite dimensional Cartan subalgebra. In this paper, a sufficient condition for LieN-derivation algebra ofLco-inciding with Lie derivation algebra ofLis given. As applications, anyN-derivationof Schr ̈odinger-Virasoro algebra, generalized Witt algebras, Kac-Moody algebrasand their Borel subalgebras, is a derivation.