The structure of the group G(k[t]): Variations on a theme of Soulé

Abstract

Following Soule’s ideas [14] we give a presentation of the abstract group G(k[t]) for any semisimple (connected) simply connected absolutely almost simple k–group G. 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 coincide.