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

We reformulate maximal D = 5 supergravity in the consistent approach uniquely based on free differential algebras and the solution of their Bianchi identities (i.e. the 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 of the existence of a Lagrangian. The use of free differential algebras is essential to clarify, within a cohomological set-up, the dualization mechanism between 1- and 2-forms. Our theories contain 12-r self-dual 2-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 to domain wall solutions and the trapping of gravity.