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Recently it was shown that standard odd- and even-dimensional general relativity can be obtained from a $$(2n+1)$$ ( 2 n + 1 ) -dimensional Chern–Simons Lagrangian invariant under the $$B_{2n+1}$$ B 2 n + 1 algebra and from a $$(2n)$$ ( 2 n ) -dimensional Born–Infeld Lagrangian invariant under a subalgebra $${\mathcal {L}}^{B_{2n+1}}$$ L B 2 n + 1 ,...