Buildings and shadows
type: Item
instance of: scholarly article
title: Buildings and shadows
zbMATH Open document ID: 0531.20025
DOI: 10.1007/BF02189594
author: Betty Salzberg
published in: Aequationes Mathematicae
publication date: 1982-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/136943
review text: This expository paper describes the geometries associated to simle Lie groups, following J. Tits' theory of buildings and shadows. First the definitions of ''building'', ''apartment'', ''Dynkin-diagram'' are given and motivated. Then the author describes the buildings and the associated geometries for the classical groups and for \(G_ 2\). In the last two chapters ''shadows'' are defined in order to investigate the geometries of the exceptional groups. The shadow geometry for \(E_ 8\) is explicitly derived.
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 51E30
Mathematics Subject Classification ID: 14L35
zbMATH DE Number: 3842131
zbMATH Keywords: geometries of exceptional groups
zbMATH Keywords: simle Lie groups
zbMATH Keywords: buildings
zbMATH Keywords: shadows
zbMATH Keywords: Dynkin-diagram
reviewed by: F. Pauer
MaRDI profile type: Publication
cites work: Buildings of spherical type and finite BN-pairs
cites work: Diagrams for geometries and groups
cites work: Q5662096
cites work: Sur certains groupes simples
cites work: Discrete groups generated by reflections
cites work: Q5566193
cites work: Q3236268
description: scientific article; zbMATH DE number 3842131