Please use this identifier to cite or link to this item: https://doi.org/10.21256/zhaw-1735
Title: Smooth Hughes planes are classical
Authors : Bödi, Richard
Published in : Archiv der Mathematik
Volume(Issue) : 73
Issue : 1
Pages : 73
Pages to: 80
Publisher / Ed. Institution : Springer
Publisher / Ed. Institution: Basel
Issue Date: Jul-1999
License (according to publishing contract) : Licence according to publishing contract
Type of review: Peer review (Publication)
Language : English
Subjects : Complex number; Projective plane; Collineation group; Classical plane; Compact projective plane
Subject (DDC) : 500: Natural sciences and mathematics
Abstract: We prove that the only compact projective Hughes planes which are smooth projective planes are the classical planes over the complex numbers C, the quaternions H, and the Caley numbers O. As a by-product this shows that an 8-dimensional smooth projective plane which admits a collineation group of dimension d≥17 is isomorphic to the quaternion projective plane P 2 H. For topological compact projective planes this is true if d≥19, and this bound is sharp.
Further description : Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)
Departement: School of Engineering
Publication type: Article in scientific Journal
DOI : 10.1007/s000130050022
10.21256/zhaw-1735
ISSN: 0003-889X
URI: https://digitalcollection.zhaw.ch/handle/11475/3229
Appears in Collections:Publikationen School of Engineering

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