Kac-Moody groups as discrete groups

Bertrand Remy

Published 2004-02-18Version 1

This survey paper presents the discrete group viewpoint on Kac-Moody groups. Over finite fields, the latter groups are finitely generated; they act on new buildings enjoying remarkable negative curvature properties. The study of these groups is shared between proving results supporting the analogy with some $S$-arithmetic groups, and exhibiting properties showing that they are new groups.