N-Derivations for Finitely Generated Graded Lie Algebras
Abstract
The N-derivation is a natural generalization of derivation and triple derivation. Let 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
coinciding with the Lie derivation algebra of
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.
Supported by the Natural Science Foundation of Fujian Province, China (2010J05001, 2012J01001), and the Foundation of Pre-research and Development of Fujian University of Technology (GY-Z10076).