A characterization of buildings of a spherical type
type: Item
instance of: scholarly article
title: A characterization of buildings of a spherical type
zbMATH Open document ID: 0606.51004
DOI: 10.1016/S0195-6698(86)80006-3
author: Guy Hanssens
published in: European Journal of Combinatorics
publication date: 1986-01-01T00:00:00Z
review text: In his article in Eur. J. Comb. 3, 103-118 (1982; Zbl 0504.51006), \textit{F. Buekenhout} provides an axiom system that gives all ''natural'' point- line geometries associated with spherical buildings. The aim of this paper is to simplify his list of axioms. Two main results give necessary and sufficient conditions for the geometry \(\Gamma =({\mathcal P},{\mathcal L})\) to be the geometry of points and lines of a (weak) thick building of one of the given types. The ''only if'' part can be found in literature [see for instance F. Buekenhout, given above, and \textit{A. M. Cohen} and \textit{B. N. Cooperstein}, Geom. Dedicata 15, 73-105 (1983; Zbl 0541.51010)]. The ''if'' part follows immediately by putting together Theorems 3 until 9 of the present article.
Mathematics Subject Classification ID: 51B05
zbMATH DE Number: 3979904
zbMATH Keywords: diagram
zbMATH Keywords: point-line geometries
zbMATH Keywords: spherical buildings
MaRDI profile type: Publication
cites work: Q3327250
cites work: Local recognition of Tits geometries of classical type
cites work: The structure of near polygons with quads
cites work: Q4183899
cites work: Diagrams for geometries and groups
cites work: Q3341469
cites work: An approach to building geometries based on points, lines and convexity
cites work: On the foundations of polar geometry
cites work: Dual polar spaces
cites work: On a theorem of Cooperstein
cites work: Points and Lines in Metasymplectic Spaces
cites work: An axiom system for metasymplectic spaces
cites work: A characterization of some geometries of Lie type
cites work: A characterization of some Lie incidence structures
cites work: A characterization of point-line geometries for finite buildings
cites work: Near \(n\)-gons and line systems
cites work: Q3923180
cites work: Buildings of spherical type and finite BN-pairs
cites work: Q3961400
cites work: Q3263163
full work available at URL: s0195-6698(86)80006-3
OpenAlex ID: W2056739869
description: scientific article; zbMATH DE number 3979904