  We show that the so-called semi-simple extended Poincar\'{e} (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.
