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

2002/12/31 by Jose A. de Azcarraga, Jose M. Izquierdo, Moises Picon +1 · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.DG #math.GR #math.MP

paper · pdf · doi:10.1016/s0550-3213(03)00342-0

published as Nucl.Phys. B662 (2003) 185-219 · 37 pages, Plain Latex, 30-Dec-02

arxiv created 2002/12/31 · arxiv updated 2009/11/30

Abstract

We study how to generate new Lie algebras G(N₀,..., 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 λ which rescales the coordinates of the Lie (super)group G, g^i_p → λ^p g^i_p, in a way subordinated to the splitting of G as a sum V₀ ⊕ ... ⊕ V_p ⊕ ... ⊕ V_n 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.

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