Topological groups of Kac-Moody type, Fuchsian twinnings and their lattices

2002/05/04 by Bertrand Remy, Remy, Bertrand, Mark Ronan +1
Mathematics · #17B67 #20E42 #20G25 #22E40 #51E24 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:17B67 #msc:20E42 #msc:20G25 #msc:22E40 #msc:51E24

paper · pdf · doi:10.48550/arxiv.math/0205038

33 pages, 3 figures

arxiv created 2002/05/04 · arxiv updated 2009/11/30

Abstract

This paper deals with a class of totally disconnected groups acting on buildings, among which are certain Kac-Moody groups. The apartments of our buildings are hyperbolic planes tiled by right-angled polygons. We discuss linearity properties for the groups, as well as an analogy with semisimple groups over local fields of positive characteristic. Looking for counter-examples to this analogy leads to the construction of Moufang twinnings "with several ground fields".

Related

• Structures immobilières pour un groupe de Kac-Moody sur un corps local
• Loop groups and twin buildings
• Kac-Moody groups: split and relative theories. Lattices
• Kac-Moody groups, analytic regularity conditions and cities
• Topological simplicity, commensurator super-rigidity and non-linearities of Kac-Moody groups