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

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 $S_H$-expanded algebras where $S=Z_{2n}$. The invariant tensors for $S_H$-expanded algebras are calculated and the dual formulation of $S_H$-expansion procedure is proposed. We consider the $S_H$-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 $S_H$-expanded is constructed and its relationship to the general relativity is studied.

31 pages, no figures

References in corpus (9)

• Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity
• Expanding Lie (super)algebras through abelian semigroups
• Standard General Relativity from Chern-Simons Gravity
• Wess-Zumino term for the AdS superstring and generalized Inonu-Wigner contraction
• Expansions of algebras and superalgebras and some applications
• Lecture notes on Chern-Simons (super-)gravities. Second edition (February 2008)
• Extensions, expansions, Lie algebra cohomology and enlarged superspaces
• The Extended Cartan Homotopy Formula and a Subspace Separation Method for Chern--Simons Theory
• Dual Formulation of the Lie Algebra S-expansion Procedure

Cited by in corpus (18)

• Pure Lovelock gravity and Chern-Simons theory
• Chern-Simons Supergravity in D=3 and Maxwell superalgebra
• On the Hidden Maxwell Superalgebra underlying D=4 Supergravity
• New family of Maxwell like algebras
• Lovelock gravities from Born-Infeld gravity theory
• $\mathcal{N}$-extended Maxwell supergravities as Chern-Simons theories in three spacetime dimensions
• Generalized supersymmetric cosmological term in N=1 Supergravity
• Three-dimensional Poincaré supergravity and $\mathcal{N}$-extended supersymmetric BMS${}_3$ algebra
• Semi-simple enlargement of the ${\mathfrak{bms}}_3$ algebra from a $\mathfrak{so}(2,2)\oplus \mathfrak{so}(2,1)$ Chern-Simons theory
• An Analytic Method for $S$-Expansion involving Resonance and Reduction
• Infinite S-Expansion with Ideal Subtraction and Some Applications
• Resonant algebras and gravity
• The Maxwell group in 2+1 dimensions and its infinite-dimensional enhancements
• Chern-Simons Gravity in Four Dimensions
• On a Java library to perform S-expansions of Lie algebras
• A Java library to perform S-expansions of Lie algebras
• Five dimensional Chern-Simons Gravity for the expanded (anti)-de Sitter gauge group C${}_5$
• Scalar-tensor theory with EGB term from Einstein Chern-Simons gravity