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Recently was shown that standard odd and even-dimensional General Relativity can be obtained from a $(2n+1)$-dimensional Chern-Simons Lagrangian invariant under the $B_{2n+1}$ algebra and from a $(2n)$-dimensional Born-Infeld Lagrangian invariant under a subalgebra $\cal{L}^{B_{2n+1}}$ respectively.
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