On Derivations of Parabolic Lie Algebras

Let g be a reductive Lie algebra over an algebraically closed, characteristic zero field or over R. Let q be a parabolic subalgebra of g.We characterize the derivations of q by decomposing the derivation algebra as the direct sum of two ideals: one of which is the image of the adjoint representation and the other consists of all linear transformations on q that map q into its center and map the derived algebra of q to 0.