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arXiv · 1311.2215

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

José Díaz·Octavio Fierro·Fernando Izaurieta·Nelson Merino·Eduardo Rodríguez·Patricio Salgado·Omar Valdivia
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Abstract

We show that the so-called semi-simple extended Poincaré (SSEP) algebra in $D$ dimensions can be obtained from the anti-de~Sitter algebra $\mathfrak{so} \left( D-1,2 \right)$ by means of the $S$-expansion procedure with an appropriate semigroup $S$. A general prescription is given for computing Casimir operators for $S$-expanded algebras, and the method is exemplified for the SSEP algebra. The $S$-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 $2+1$ dimensions.

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José Díaz, Octavio Fierro, Fernando Izaurieta, Nelson Merino, Eduardo Rodríguez, Patricio Salgado, Omar Valdivia. 2013-11-09. A generalized action for $\left( 2 + 1 \right)$-dimensional Chern--Simons gravity. https://doi.org/10.1088/1751-8113/45/25/255207

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