Abstract
We first remark that Kac–Moody groups enable us to produce hyperbolic buildings – automatically endowed with nonuniform lattices. The main result then deals with groups whose buildings are trees or two-dimensional hyperbolic. It is a factorization theorem for abstract isomorphisms. It shows the existence of nonisomorphic Kac–Moody groups with the same associated isomorphism class of buildings.
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Rémy, B. Immeubles de Kac–Moody hyperboliques, groupes non isomorphes de même immeuble (Hyperbolic Kac–Moody Buildings Nonisomorphic Groups with the Same Building) . Geometriae Dedicata 90, 29–44 (2002). https://doi.org/10.1023/A:1014969911151
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DOI: https://doi.org/10.1023/A:1014969911151