A generalized action for(2 + 1)-dimensional Chern–Simons gravity

Abstract

We show that the so-called semi-simple extended Poincar ́e (SSEP) algebra inDdimensions canbe obtained from the anti-de Sitter algebraso(D−1,2) by means of theS-expansion procedurewith an appropriate semigroupS. A general prescription is given for computing Casimir operatorsforS-expanded algebras, and the method is exemplified for the SSEP algebra. TheS-expansionmethod also allows us to extract the corresponding invariant tensor for the SSEP algebra, whichis a key ingredient in the construction of a generalized action for Chern–Simons gravity in 2 + 1dimensions.