English

A generalized action for $\left( 2 + 1 \right)$-dimensional Chern--Simons gravity

General Relativity and Quantum Cosmology 2013-11-12 v1 Mathematical Physics math.MP

Abstract

We show that the so-called semi-simple extended Poincar\'{e} (SSEP) algebra in DD dimensions can be obtained from the anti-de~Sitter algebra so(D1,2)\mathfrak{so} \left( D-1,2 \right) by means of the SS-expansion procedure with an appropriate semigroup SS. A general prescription is given for computing Casimir operators for SS-expanded algebras, and the method is exemplified for the SSEP algebra. The SS-expansion method also allows us to extract the corresponding invariant tensor for the SSEP algebra, which is a key ingredient in the construction of a generalized action for Chern--Simons gravity in 2+12+1 dimensions.

Cite

@article{arxiv.1311.2215,
  title  = {A generalized action for $\left( 2 + 1 \right)$-dimensional Chern--Simons gravity},
  author = {José Díaz and Octavio Fierro and Fernando Izaurieta and Nelson Merino and Eduardo Rodríguez and Patricio Salgado and Omar Valdivia},
  journal= {arXiv preprint arXiv:1311.2215},
  year   = {2013}
}
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