Chamber systems with string diagrams
type: Item
instance of: scholarly article
title: Chamber systems with string diagrams
zbMATH Open document ID: 0567.51009
DOI: 10.1007/BF00147758
author: F. G. Timmesfeld
author: Thomas Meixner
published in: Geometriae Dedicata
publication date: 1983-01-01T00:00:00Z
review text: There are two (canonical) constructions to get a Tits geometry \(\Gamma\) (\({\mathcal C})\) out of a chamber system \({\mathcal C}\) (both over the same set I) and, vice-versa, a chamber system \({\mathcal C}(\Gamma)\) from a Tits geometry \(\Gamma\). These two constructions are, in general, not inverse to each other, i.e. \({\mathcal C}(\Gamma ({\mathcal C}))\) and \({\mathcal C}\) need not be canonically isomorphic, nor do \(\Gamma\) (\({\mathcal C}(\Gamma))\) and \(\Gamma\). The authors give a sufficient condition in order to which the previous isomorphisms occur and, also, the diagrams of \({\mathcal C}\) and \(\Gamma\) (\({\mathcal C})\) coincide. Moreover, under this condition each flag of \(\Gamma\) (\({\mathcal C})\) is contained in a flag of type I and, if G is a group of automorphisms acting transitively on \({\mathcal C}\), then G is flag- transitive on \(\Gamma\) (\({\mathcal C}).\) At the end of the article the authors give some examples showing how the above results may be used.
Mathematics Subject Classification ID: 51D20
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 51E25
zbMATH DE Number: 3905331
zbMATH Keywords: flag transitive group
zbMATH Keywords: Tits geometry
zbMATH Keywords: chamber system
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00147758
OpenAlex ID: W2011170923
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description: scientific article; zbMATH DE number 3905331