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

DOI10.1016/S0550-3213(03)00342-0zbMATH Open1022.22022arXivhep-th/0212347MaRDI QIDQ1810380

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Publication date: 3 June 2003

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Abstract: We study how to generate new Lie algebras $mathcalG(N_0,\mathrm{...},N_p,\mathrm{...},N_n)$ from a given one $mathcalG$. 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 $G$, $g^{i_p}olambd{a}^p{g}^{i_p}$, in a way subordinated to the splitting of $mathcalG$ as a sum $V_{0}oplus\mathrm{...}oplus{V}_{p}oplus\mathrm{...}oplus{V}_n$ 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.

Full work available at URL: https://arxiv.org/abs/hep-th/0212347

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