Abstract
Departing from a Moufang set related to a polarity in an exceptional Moufang quadrangle of type , we construct a rank three geometry. The main property of this new geometry is that its automorphism group is identical to the one of the underlying Moufang set, providing a tool to study this Moufang set in a geometrical way. As a corollary we obtain that every automorphism of an exceptional Moufang quadrangle of type stabilizing the absolute points of a polarity, also centralizes the polarity. This handles the final case of a similar result for all polarities of Moufang -gons with .
Citation
Koen Struyve. "Moufang sets related to polarities in exceptional Moufang quadrangles of type $\mathsf{F}_4$." Innov. Incidence Geom. 10 121 - 132, 2009. https://doi.org/10.2140/iig.2009.10.121
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