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

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arxiv hep-th/0212347 v1 pith:FNPUX5PR submitted 2002-12-31 hep-th math-phmath.DGmath.GRmath.MP

Jose A. de Azcarraga , Jose M. Izquierdo , Moises Picon , Oscar Varela This is my paper · ORCID
classification hep-thmath-phmath.DGmath.GRmath.MP
keywords algebrasoplusmathcalsuperchern-simonsdifferentialexpandingfree
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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 \.In\"on\"u-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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Cited by 3 Pith papers

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    hep-th 2019-08 conditional novelty 6.0 of 10

    New infinite-dimensional superalgebras, the deformed and enlarged super-BMS3 algebras for N=1,2,4, are produced by S-expanding super-Virasoro and are related by a flat limit.

  3. An Introduction to String Newton-Cartan Holography and Integrability

    hep-th 2026-03 accept novelty 3.0 of 10

    String Newton-Cartan holography, the non-relativistic limit of the AdS/CFT correspondence, is organized and reviewed around five consistency conditions, with its classical solutions, spectrum, and integrability structure.

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