Characterizing symplectic quadrangles by their derivations
type: Item
instance of: scholarly article
title: Characterizing symplectic quadrangles by their derivations
zbMATH Open document ID: 0761.51004
DOI: 10.1007/BF01198648
author: Andreas E. Schroth
published in: Archiv der Mathematik
publication date: 1992-09-27T00:00:00Z
review text: The author shows that a generalized quadrangle \({\mathcal Q}\) is isomorphic to the geometry of absolute points and lines with respect to a symplectic polarity of a 3-dimensional projective space if and only if the derivation at every point of \({\mathcal Q}\) yields a projective plane. The proof is achieved as a nice application of the axiom system of Winternitz. Furthermore, the author examines the case of locally compact connected quadrangles more closely and gives several characterizations of the symplectic quadrangles over the fields \(\mathbb{R}\) and \(\mathbb{C}\).
Mathematics Subject Classification ID: 51E12
Mathematics Subject Classification ID: 51H15
zbMATH DE Number: 62258
zbMATH Keywords: symplectic quadrangles
zbMATH Keywords: derivations
zbMATH Keywords: locally compact connected quadrangles
reviewed by: Norbert Knarr
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 62258