nilpotent radical vs killing-orthogonal complement

i'm beginning to suspect that one aspect of the relationship between nilpotent radicals and killing-orthogonal complements of parabolic subalgebras is that there's some nice geometric interpretation of the way in which the subalgebra can be expressed as a semi-direct product of the infinitesimal automorphism lie algebra of the "residual geometry" acting on a killing-orthogonal complement (or nilpotent radical).