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 dimensions can be obtained from the anti-de~Sitter algebra by means of the -expansion procedure with an appropriate semigroup . A general prescription is given for computing Casimir operators for -expanded algebras, and the method is exemplified for the SSEP algebra. The -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 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}
}