Non-Semisimple Gaugings of D=5 N=8 Supergravity and FDA.s

We reformulate maximal D=5 supergravity in the consistent approach uniquely based on Free Differential Algebras and the solution of their Bianchi identities (= rheonomic method). In this approach the lagrangian is unnecessary since the field equations follow from closure of the supersymmetry algebra. This enables us to explicitly construct the non-compact gaugings corresponding to the non--semisimple algebras CSO(p,q,r), irrespectively from the existence of a lagrangian. The use of Free Differential Algebras is essential to clarify, within a cohomological set up, the dualization mechanism between one-forms and two-forms. Our theories contain 12-r self-dual two-forms and 15+r gauge vectors, r of which are abelian and neutral. These theories, whose existence is proved and their supersymmetry algebra constructed hereby, have potentially interesting properties in relation with domain wall solutions and the trapping of gravity.