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Exceptional Moufang Quadrangles of Type F4

Published online by Cambridge University Press:  20 November 2018

Bernhard Mühlherr  and
Hendrik Van Maldeghem
Bernhard Mühlherr
Affiliation:
Fachbereich Mathematik, Lehrstuhl II, Universitӓt Dortmund, D-44221 Dortmund, Germany email: bernhard.muehlherr@mathematik.uni-dortmund.de
Hendrik Van Maldeghem
Affiliation:
Vakgroep voor Zuivere Wiskunde en Computeralgebra, Universiteit Gent, Galglaan 2, B-9000 Gent, Belgium email: hvm@cage.rug.ac.be
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Abstract

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In this paper, we present a geometric construction of the Moufang quadrangles discovered by Richard Weiss (see Tits & Weiss [18] or Van Maldeghem [19]). The construction uses fixed point free involutions in certain mixed quadrangles, which are then extended to involutions of certain buildings of type ${{F}_{4}}$. The fixed flags of each such involution constitute a generalized quadrangle. This way, not only the new exceptional quadrangles can be constructed, but also some special type of mixed quadrangles.

Keywords

51E1251E24
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 2 , 01 April 1999 , pp. 347 - 371
Copyright
Copyright © Canadian Mathematical Society 1999

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