Group algebras of Kleinian type and groups of units

Details Group algebras of Kleinian type and groups of units Group algebras of Kleinian type and groups of units

2007-01-12

arxiv.org/abs/math/0701351v1

Mathematics

Representation Theory

12 pages

Scientific paper

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.

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