Vol. 3, No. 4, 2009

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The structure of the group {\slshape\bfseries G}(\kern-.1emk\/[t\kern.1em]): Variations on a theme of Soulé

Benedictus Margaux

Vol. 3 (2009), No. 4, 393–409
Abstract

Following Soulé’s ideas from 1979, we give a presentation of the abstract group  G(k[t]) for any semisimple (connected) simply connected absolutely almost simple k-group  G(k[t]). As an application, we give a description of  G(k[t]) in terms of direct limits, and show that the Whitehead group and the naive group of connected components of  G(k[t]) coincide.

Keywords
Bruhat–Tits buildings, arithmetic groups, simplicial fundamental domain
Mathematical Subject Classification 2000
Primary: 20G10
Secondary: 20F05
Milestones
Received: 19 November 2007
Revised: 5 November 2008
Accepted: 11 November 2008
Published: 15 June 2009
Authors
Benedictus Margaux