Semi-simple Lie algebras are determined by their Iwasawa subalgebras

Using tools from the geometry of Einstein solvmanifolds, we give a geometric argument that a semi-simple Lie algebra (of non-compact type) is completely determined by its Iwasawa subalgebra. Furthermore, we produce an algebraic procedure for recovering the semi-simple (of non-compact type) from its Iwasawa subalgebra.