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

By J. A. Azcárraga, J. M. Izquierdo, M. Picon, O. Varela. 2002

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Abstract 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 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 V 0 ⊕⋯⊕ V p ⊕⋯⊕ 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/9b8c2275354fc64c170e9ecf8026332d1fae762f