Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chem-Simons supergravity

We study how to generate new Lie algebras G(N-0,..., N-p,..., N-n) from a given one G. The (order by order) method consists in expanding its Maurer-Cartan one-forms in powers of a real parameter lambda which rescales the coordinates of the Lie (super)group G, g(i)p --> lambda(p)g(i)p, in a way subordinated to the splitting of G as a sum V-0 circle plus ... circle plus V-p circle plus ... circle plus V-n of vector subspaces. We also show that, under certain conditions, one of the obtained algebras may correspond to a generalized Inonu-Wigner contraction in the sense of Weimar-Woods, but not in general. The method is used to derive the M-theory superalgebra, including its Lorentz part, from osp(1\32). It is also extended to include gauge free differential (super)algebras and Chern-Simons theories, and then applied to D = 3 CS supergravity. (C) 2003 Elsevier Science B.V. All rights reserved.