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The N-derivation is a natural generalization of derivation and triple derivation. Let [Formula: see text] 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 [Formula: see text] coinciding with the Lie derivation algebra of [Formula: see text] is given. As applications, any N-derivation of the Schrödinger-Virasoro algebra, generalized Witt algebra, Kac-Moody algebra or their Borel subalgebra is a derivation.

N-Derivations for Finitely Generated Graded Lie Algebras