  Let $\Gamma$ be a lattice in a connected semisimple Lie group $G$ with
trivial center and no compact factors. We introduce a volume invariant for
representations of $\Gamma$ into $G$, which generalizes the volume invariant
for representations of uniform lattices introduced by Goldman. Then, we show
that the maximality of this volume invariant exactly characterizes discrete,
faithful representations of $\Gamma$ into $G$ except for $\Gamma\subset
\mathrm{PSL_2 \mathbb{C}}$ a nonuniform lattice.
