Generalized Lie triple derivations.

Let [image omitted] be a complex semisimple Lie algebra, [image omitted] be a Borel subalgebra of [image omitted] and [image omitted] denote the maximal nilpotent subalgebra of [image omitted]. In this article, we prove that every generalized Lie triple derivation of [image omitted] 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 [image omitted] of each classical complex simple Lie algebra is the sum of a Lie triple derivation and a homothety. [ABSTRACT FROM AUTHOR]