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Exceptional Moufang Quadrangles of Type $\mathsf{F}_4$ |
Canad. J. Math. 51(1999), 347-371
Published:1999-04-01
Printed: Apr 1999
Printed: Apr 1999
- Bernhard Mühlherr
- Hendrik Van Maldeghem
Abstract
In this paper, we present a geometric construction of the Moufang
quadrangles discovered by Richard Weiss (see Tits \& Weiss
\cite{Tit-Wei:97} or Van Maldeghem \cite{Mal:97}). The construction
uses fixed point free involutions in certain mixed quadrangles, which
are then extended to involutions of certain buildings of type
$\ssF_4$. 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.
| MSC Classifications: |
51E12 - Generalized quadrangles, generalized polygons 51E24 - Buildings and the geometry of diagrams |