  The algebras of Kleinian type are finite dimensional semisimple rational
algebras $A$ such that the group of units of an order in $A$ is commensurable
with a direct product of Kleinian groups. We classify the Schur algebras of
Kleinian type and the group algebras of Kleinian type. As an application, we
characterize the group rings $RG$, with $R$ an order in a number field and $G$
a finite group, such that $RG^*$ is virtually a direct product of free-by-free
groups.
