Non-semisimple gaugings of D=5, N=8 supergravity and FDAs

We reformulate maximal D = 5 supergravity in the consistent approach unique ly based on free differential algebras and the solution of their Bianchi id entities (i.e, the rheonomic method). In this approach the Lagrangian is un necessary since the field equations follow from closure of the supersymmetr y algebra. This enables us to explicitly construct the non-compact gaugings corresponding to the non-semisimple algebras CSO(p, q, r), irrespectively of the existence of a Lagrangian. The use of free differential algebras is essential to clarify, within a cohomological set-up, the dualization mechan ism between 1- and 2-forms. Our theories contain 12 - r self-dual 2-forms a nd 15 + r gauge vectors, r of which are Abelian and neutral. These theories , whose existence is proved and their supersymmetry algebra constructed her eby, have potentially interesting properties in relation to domain wall sol utions and the trapping of gravity.