Regular spreads and chain geometries
type: Item
instance of: scholarly article
title: Regular spreads and chain geometries
zbMATH Open document ID: 0959.51005
author: Andrea Blunck
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2001-04-24T00:00:00Z
review text: A translation plane \({\mathcal A}\) can be constructed from a spread \(S\) of a projective space over a not necessarily commutative field \(K\). In [\textit{T. Grundhöfer}, Geom. Dedicata 11, 227-237 (1981; Zbl 0492.51003)], it was proved that (if \(|K|> 2\)) \(S\) is regular if and only if \({\mathcal A}\) is a Moufang plane and \(K\) is contained in the center of its coordinate alternative field. The author gives a new proof of this theorem by means of chain geometries (= certain incidence structures constructed from associative algebras).
reviewed by: Bart De Bruyn
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 51A45
Mathematics Subject Classification ID: 51B05
Mathematics Subject Classification ID: 51B10
zbMATH DE Number: 1421347
zbMATH Keywords: regulus
zbMATH Keywords: spread
zbMATH Keywords: translation plane
zbMATH Keywords: chain geometry
zbMATH Keywords: Jordan system
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1421347