Group algebras of Kleinian type and groups of units

Gabriela Olteanu; Angel del Rio

Group algebras of Kleinian type and groups of units

Representation Theory 2007-05-23 v1 Group Theory

Authors: Gabriela Olteanu , Angel del Rio

Abstract

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.

Keywords

kleinian type algebras group algebras units of orders schur algebras kleinian groups group rings

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@article{arxiv.math/0701351,
  title  = {Group algebras of Kleinian type and groups of units},
  author = {Gabriela Olteanu and Angel del Rio},
  journal= {arXiv preprint arXiv:math/0701351},
  year   = {2007}
}

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12 pages

Group algebras of Kleinian type and groups of units

Abstract

Keywords

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