2025/08/12 by Guy Rousseau, Rousseau, Guy
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.2508.08728
openalex publication_date 2025/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a split Kac-Moody group (in J. Tits' definition) over a field endowed with a real valuation, we build an ordered affine hovel on which the group acts. This construction generalizes the one already done by S. Gaussent and the author when the residue field contains the complex field and the one by F. Bruhat and J. Tits when the group is reductive. We prove that this hovel has all the properties of ordered affine hovels (masures affines ordonnées) as defined previously by the author. We use the maximal Kac-Moody group as defined by O. Mathieu and we prove a few new results about it over any field; in particular we prove, in some cases, a simplicity result for this group. At the end an erratum corrects a mistake in the counter-example of 4.12 3 (c).