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Exceptional Moufang Quadrangles of Type $\mathsf{F}_4$

Open Access article
 Printed: Apr 1999
  • Bernhard Mühlherr
  • Hendrik Van Maldeghem
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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, 51E24 show english descriptions Generalized quadrangles, generalized polygons
Buildings and the geometry of diagrams
51E12 - Generalized quadrangles, generalized polygons
51E24 - Buildings and the geometry of diagrams

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