Kac-Moody groups as discrete groups

2004/02/18 by Bertrand Rémy, Bertrand Remy, Remy, Bertrand
Mathematics · #17B67 #22E20 #22E40 #22F50 #51E24 #53C24 #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:17B67 #msc:22E20 #msc:22E40 #msc:22F50 #msc:51E24 #msc:53C24

paper · pdf · doi:10.48550/arxiv.math/0402300

15 pages, conference

arxiv created 2004/02/18 · openalex publication_date 2004/02/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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