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Compact 16-Dimensional Projective Planes with Large Collineation Groups. IV

Published online by Cambridge University Press:  20 November 2018

Helmut Salzmann
Helmut Salzmann*
Affiliation:
Universität Tübingen, Tubingen, Germany
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Let be a topological projective plane with compact point set P of finite (covering) dimension. In the compact-open topology (of uniform convergence), the group Σ of continuous collineations of is a locally compact transformation group of P.

THEOREM. If dim Σ > 40, thenis isomorphic to the Moufang plane 6 over the real octonions (and dim Σ = 78).

By [3] the translation planes with dim Σ = 40 form a one-parameter family and have Lenz type V. Presumably, there are no other planes with dim Σ = 40, cp. [17].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 4 , 01 August 1987 , pp. 908 - 919
Copyright
Copyright © Canadian Mathematical Society 1987

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