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We show that the so-called semi-simple extended Poincar\'{e} (SSEP) algebrain $D$ dimensions can be obtained from the anti-de~Sitter algebra$\mathfrak{so} \left( D-1,2 \right)$ by means of the $S$-expansion procedurewith an appropriate semigroup $S$. A general prescription is given forcomputing Casimir operators for $S$-expanded algebras, and the method isexemplified for the SSEP algebra. The $S$-expansion method also allows us toextract the corresponding invariant tensor for the SSEP algebra, which is a keyingredient in the construction of a generalized action for Chern--Simonsgravity in $2+1$ dimensions.

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