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

We propose a modification to the Lie algebra SS-expansion method. The modification is carried out by imposing a condition on the SS-expansion procedure, when the semigroup is given by a cyclic group of even order. The SS-expanded algebras are called SHSH-expanded algebras where S=Z2nS=Z2n. The invariant tensors for SHSH-expanded algebras are calculated and the dual formulation of SHSH-expansion procedure is proposed. We consider the SHSH-expansion of the five-dimensional AdSAdS algebra and its corresponding invariants tensors are found. Then a Chern–Simons Lagrangian invariant under the five-dimensional AdSAdS algebra SHSH-expanded is constructed and its relationship to the general relativity is studied.