Classical and Non-Linearity Properties of Kac-Moody Lattices

  • Bertrand Rémy


This paper presents a new class of geometries and groups satisfying algebraic and combinatorial rules. These were initially produced in the context of Kac-Moody theory to obtain infinite-dimensional analogues of semisimple algebraic groups. Adopting the point of view of discrete groups, we obtain in this way lattices for buildings which are both negatively curved and have dimension at least two, properties which are incompatible for Euclidean buildings. The problem then is to know to what extent the groups are new and whether classical properties of lattices of Lie groups are relevant. The first question leads to discussing linearity properties. The second one is partially answered by positive results concerning Kazhdan property (T) and cohomological finiteness properties, proved by several authors. Our guideline is the analogy with semisimple groups over local fields of positive characteristic.


Algebraic Group Coxeter Group Semisimple Group Arithmetic Group Semisimple Algebraic Group 
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© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Bertrand Rémy
    • 1
  1. 1.Institute of MathematicsThe Hebrew UniversityJerusalemIsrael

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