A structure theorem for Leibniz homology

Presented is a structure theorem for the Leibniz homology, HL⁎, of an Abelian extension of a simple real Lie algebra g. As applications, results are stated for affine extensions of the classical Lie algebras sln(R), son(R), and spn(R). Furthermore, HL⁎(h) is calculated when h is the Lie algebra of the Poincaré group as well as the Lie algebra of the affine Lorentz group. The structure theorem identifies all of these in terms of g-invariants.