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

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.

References in corpus (2)

• Expanding Lie (super)algebras through abelian semigroups
• Semi-simple $o(N)$-extended super-Poincaré algebra

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