Group algebras of Kleinian type and groups of units

doi:10.1016/j.jalgebra.2007.03.026

Journal of Algebra

Volume 318, Issue 2, 15 December 2007, Pages 856-870

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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 the group of units of RG is virtually a direct product of free-by-free groups.

Keywords

Group algebras

Kleinian groups

Groups of units

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^☆: Research supported by M.E.C. of Romania (CEEX-ET 47/2006), D.G.I. of Spain and Fundación Séneca of Murcia.

¹: Current address: Department of Mathematics, University of Murcia, 30100 Murcia, Spain.

Journal of Algebra

Group algebras of Kleinian type and groups of units☆

Abstract

Keywords