Topological pseudo-ovals, elation Laguerre planes, and elation generalized quadrangles
type: Item
instance of: scholarly article
title: Topological pseudo-ovals, elation Laguerre planes, and elation generalized quadrangles
zbMATH Open document ID: 0806.51009
DOI: 10.1007/BF02572326
author: Rainer Löwen
published in: Mathematische Zeitschrift
publication date: 1994-12-21T00:00:00Z
full work available at URL: https://eudml.org/doc/174655
review text: We introduce the notion of (topological) pseudo-ovals. They provide the key to a fuller understanding of Steinke's non-classical 4-dimensional Laguerre planes [\textit{G. F. Steinke}, `Eine Klassifikation 4- dimensionaler Laguerre-Ebenen mit großer Automorphismengruppe', Habil.-Sch. (1988); see also Forum Math. 2, 233-247 (1990; Zbl 0696.51008)] and of their relationships with other geometric structures. Roughly speaking, a pseudo-oval is a sufficiently large family of translation planes sitting on different \(2n\)-dimensional subspaes of one \(3n\)-dimensional vector space, such that the intersection of any two translation planes is a line in both of them. Finite analogues have been studied [see \textit{S. E. Payne} and \textit{J. A. Thas}, `Finite generalized quadrangles', Res. Notes Math., 110. (1984; Zbl 0551.05027), 8.7]. [There is a misprint in may paper: In the second matrix displayed on page 360, the third term of the bottom line should read \(-{1 \over 5} a(c + a^ 2)\)].
reviewed by: Rainer Löwen
Mathematics Subject Classification ID: 51H15
Mathematics Subject Classification ID: 51B15
Mathematics Subject Classification ID: 22D05
zbMATH DE Number: 704922
zbMATH Keywords: pseudo-ovals
MaRDI profile type: Publication
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OpenAlex ID: W2001855352
description: scientific article; zbMATH DE number 704922