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

Abstract

We study how to generate new Lie algebras $\mathcal{G}(N_0,...,N_p,...,N_n)$ from a given one $\mathcal{G}$. 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 $G$, $g^{i_p}\to {\lambda }^p{g}^{i_p}$, in a way subordinated to the splitting of $\mathcal{G}$ as a sum $V_0\oplus ...\oplus V_p\oplus ...\oplus V_n$ 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.

37 pages, Plain Latex, 30-Dec-02

References in corpus (20)

• Type IIB superstring action in AdS_5 x S^5 background
• Gauge Invariant Formulations of Lineal Gravity
• M-theory from its superalgebra
• M-Theory as a Holographic Field Theory
• Cohomology of Lie superalgebras and of their generalizations
• New Gauge Supergravity in Seven and Eleven Dimensions
• S-Theory
• The geometry of branes and extended superspaces
• The M-Algebra
• BPS states in M-theory and twistorial constituents
• Super p-Brane Theories and New Spacetime Superalgebras
• Cayley-Klein Algebras as Graded Contractions of so(N+1)
• Quantization of the Gravitational Constant in Odd-Dimensional Gravity
• Fundamental Extended Objects for Chern-Simons Supergravity
• Wess-Zumino term for AdS superstring
• The linear spectrum of OSp(32|1) Chern-Simons supergravity in eleven dimensions
• Topological Two Dimensional Dilaton Supergravity
• Considerations on Super Poincare Algebras and their Extensions to Simple Superalgebras
• Lie Superalgebra Stability and Branes
• Extensions of super Lie algebras

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