Roots in 2-spherical apartments
type: Item
instance of: scholarly article
title: Roots in 2-spherical apartments
zbMATH Open document ID: 1252.51006
author: Jean Gutt
author: Bernhard Mühlherr
publication date: 2012-05-11T00:00:00Z
Mathematics Subject Classification ID: 51E24
Mathematics Subject Classification ID: 20F55
zbMATH DE Number: 6033003
zbMATH Keywords: 2-spherical buildings
zbMATH Keywords: 2-spherical Coxeter complex
zbMATH Keywords: Moufang property
MaRDI profile type: Publication
full work available at URL: advgeom.2011.045
OpenAlex ID: W2081816900
cites work: Gated sets in metric spaces
cites work: Local to global structure in twin buildings
DOI: 10.1515/ADVGEOM.2011.045
published in: Advances in Geometry
review text: A key element of the geometry of higher rank spherical buildings, which can be used to classify them, is that they have the Moufang property. This property follows from an extension result, which roughly asserts that the global geometry of the building is determined by its local structure.NEWLINENEWLINEThe latter property is known to hold in the much broader context of \(2\)-spherical buildings: their Weyl group has the property that the order of the composition of two simple reflections is always finite. The object of this paper is to develop the tools leading to a possible proof that this implies that these buildings are Moufang. The main result is a connectivity property of the \(2\)-interior of a root \(\alpha\) (i.e. the set of \(2\)-residues stricly contained in \(\alpha\)).
reviewed by: Jean Lécureux
description: scientific article; zbMATH DE number 6033003