Please use this identifier to cite or link to this item: https://doi.org/10.21256/zhaw-1741
Title: 16-dimensional smooth projective planes with large collineation groups
Authors : Bödi, Richard
Published in : Geometriae Dedicata
Volume(Issue) : 72
Issue : 3
Pages : 283
Pages to: 298
Publisher / Ed. Institution : Springer
Publisher / Ed. Institution: Wien
Issue Date: Oct-1998
License (according to publishing contract) : Licence according to publishing contract
Type of review: Peer review (Publication)
Language : English
Subjects : Smooth projective; Plane homogeneity; 16-dimensional
Subject (DDC) : 500: Natural sciences and mathematics
Abstract: Smooth projective planes are projective planes defined on smooth manifolds (i.e. the set of points and the set of lines are smooth manifolds) such that the geometric operations of join and intersection are smooth. A systematic study of such planes and of their collineation groups can be found in previous works of the author. We prove in this paper that a 16-dimensional smooth projective plane which admits a collineation group of dimension d ≥ 39 is isomorphic to the octonion projective plane P2 O. For topological compact projective planes this is true if d ≥ 41. Note that there are nonclassical topological planes with a collineation group of dimension 40.
Further description : Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)
Departement: School of Engineering
Publication type: Article in scientific Journal
DOI : 10.1023/A:1005020223604
10.21256/zhaw-1741
ISSN: 0046-5755
URI: https://digitalcollection.zhaw.ch/handle/11475/3238
Appears in Collections:Publikationen School of Engineering

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