2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121831The 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.12 pagesRepresentation TheoryGroup Theory16S34, 20C05, 16A26, 16U60, 11R27text