Generalized Lie triple derivations

Abstract

Let be a complex semisimple Lie algebra, be a Borel subalgebra of and denote the maximal nilpotent subalgebra of . In this article, we prove that every generalized Lie triple derivation of can be written as the sum of a Lie triple derivation and a block diagonal map. We also show that every generalized Lie triple derivation for of each classical complex simple Lie algebra is the sum of a Lie triple derivation and a homothety.