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

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We study how to generate new Lie algebras G(N₀,..., Nₚ,...,Nₙ) from a given one G. The (order by order) method consists in expanding its Maurer-Cartan one-forms in powers of a real parameter λ which rescales the coordinates of the Lie (super)group G, gⁱᵖ → λᵖ gⁱᵖ, in a way subordinated to the splitting of G as a sum V₀ ⊕... ⊕ Vₚ ⊕... ⊕ Vₙ of vector subspaces. We also show that, under certain conditions, one of the obtained algebras may correspond to a generalized İnönü-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.