Ten exceptional geometries from trivalent distance regular graphs
type: Item
instance of: scholarly article
title: Ten exceptional geometries from trivalent distance regular graphs
zbMATH Open document ID: 1014.51006
DOI: 10.1007/PL00012587
published in: Annals of Combinatorics
publication date: 2003-03-27T00:00:00Z
review text: The author studies embeddings of point-line geometries \(\Gamma\) into projective spaces (mainly over the reals). In particular, it is investigated how the existence of a flag-transitive group action on \(\Gamma\) gives rise to homogeneous embeddings of \(\Gamma\) provided that \(\Gamma\) is self-polar. The results are then applied to ten exceptional small point-line geometries which arise from the classification of the trivalent distance regular graphs due to \textit{N. L. Biggs} and \textit{D. H. Smith} [Bull. Lond. Math. Soc. 3, 155-158 (1971; Zbl 0217.02404)]. These exceptional geometries include (the incidence graphs of) the Fano plane and the symplectic generalized quadrange over GF(2).
reviewed by: Michael Joswig
Mathematics Subject Classification ID: 51E26
Mathematics Subject Classification ID: 51A45
zbMATH DE Number: 1889236
zbMATH Keywords: homogeneous embeddings
zbMATH Keywords: flag transitive self-polar bislim geometries
zbMATH Keywords: real projective space
zbMATH Keywords: Coxeter graph
zbMATH Keywords: Biggs-Smith graph
zbMATH Keywords: real embedding
zbMATH Keywords: universal embedding
Wikidata QID: Q56001780
author: Hendrik Van Maldeghem
MaRDI profile type: Publication
full work available at URL: pl00012587
OpenAlex ID: W2079692794
description: scientific article; zbMATH DE number 1889236