2009/12/02 by Cyril Charignon, Charignon, Cyril
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.0912.0442
openalex publication_date 2009/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this study, we try to generalize Bruhat-Tits's theory to the case of a Kac-Moody group, that is to define an affine building for a Kac-Moody group over a local field. Actually, we will obtain a geometric space wich lacks some of the incidence properties of a building, so that it is called a hovel, following Guy Rousseau's terminology. Hovels have already been obtained for split Kac-Moody groups by Guy Rousseau and Stéphane Gaussent; here we define them for any group with a (generalized) valuated root datum, a situation wich contains the Kac-Moody groups over local fields, split and nearly split.