Einstein-Hilbert action with cosmological term from Chern-Simons gravity

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Abstract

We propose a modification to the Lie algebra S-expansion method. The modification is carried out by imposing a condition on the S-expansion procedure, when the semigroup is given by a cyclic group of even order. The S-expanded algebras are called SH-expanded algebras where S=Z2n. The invariant tensors for SH-expanded algebras are calculated and the dual formulation of SH-expansion procedure is proposed. We consider the SH-expansion of the five-dimensional AdS algebra and its corresponding invariants tensors are found. Then a Chern-Simons Lagrangian invariant under the five-dimensional AdS algebra SH-expanded is constructed and its relationship to the general relativity is studied.

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González, N., Salgado, P., Rubio, G., & Salgado, S. (2014). Einstein-Hilbert action with cosmological term from Chern-Simons gravity. Journal of Geometry and Physics, 86, 339–358. https://doi.org/10.1016/j.geomphys.2014.08.013

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