publication . Article . Other literature type . 1998

16-Dimensional Smooth Projective Planes with Large Collineation Groups

Bödi, Richard;
Open Access
  • Published: 01 Oct 1998 Journal: Geometriae Dedicata, volume 72, pages 283-297 (issn: 0046-5755, Copyright policy)
  • Publisher: Springer Nature
  • Country: Switzerland
Abstract
Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch) 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 ar...
Subjects
free text keywords: Projective plane, Topology, Projective linear group, Collineation, Projective space, Mathematical analysis, Fano plane, Real projective space, Finite geometry, Duality (projective geometry), Mathematics, Smooth projective, Plane homogeneity, 16-dimensional, 500: Naturwissenschaften und Mathematik
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