Arborescent constructions of buildings
type: Item
instance of: scholarly article
title: Arborescent constructions of buildings
zbMATH Open document ID: 1025.51014
author: Frédéric Haglund
author: Frédéric Paulin
published in: Mathematische Annalen
publication date: 2003-03-27T00:00:00Z
review text: \textit{J. Tits} classified the locally finite buildings of spherical type [`Buildings of spherical type and finite BN-pairs', Lect. Notes Math. 386, Springer-Verlag (1974; Zbl 0295.20047)] and those of Euclidean type [Lect. Notes Math. 1181, 159-190 (1986; Zbl 0611.20026)]. In both cases the set of the isomorphism classes of the buildings is countable. For buildings of hyperbolic type we have a quite different situation. A general classification theorem is not known, only some special results have been obtained. For the two-dimensional case an uncountable set of locally finite hyperbolic buildings was constructed by \textit{D. Gaboriau} and \textit{F. Paulin} [Geom. Dedicata 88, No. 1-3, 153-197 (2001; Zbl 1020.51007)]. The content of this paper is to establish an analogous result for the three-dimensional case. In order to obtain it the authors combine a classification theorem for Coxeter polytopes of spherical type and an arborescent construction of buildings of splittable Coxeter systems.
Mathematics Subject Classification ID: 51E24
Mathematics Subject Classification ID: 51F15
zbMATH DE Number: 1889248
zbMATH Keywords: locally finite buildings of spherical type
zbMATH Keywords: classification theorem for Coxeter polytopes of spherical type
zbMATH Keywords: buildings of splittable Coxeter systems
reviewed by: Wolfgang Nolte
MaRDI profile type: Publication
full work available at URL: s00208-002-0373-x
OpenAlex ID: W2068275592
DOI: 10.1007/S00208-002-0373-X
description: scientific article; zbMATH DE number 1889248