The Extended Cartan Homotopy Formula and a Subspace Separation Method for Chern--Simons Supergravity

We consider gauge field theories with a transgression form as lagrangian. Formal aspects are analyzed in full generality; the equations of motion, the boundary conditions and the conserved charges are written down for a generic Lie Algebra g. We also present a method, based on the iterative use of the Extended Cartan Homotopy Formula, which allows one to (i) systematically split the lagrangian in order to appropriately reflect the subspaces structure of the gauge algebra, and (ii) separate the lagrangian in bulk and boundary contributions. Five-dimensional Chern--Simons Supergravity is then used as an example to illustrate the method