Moufang sets related to polarities in exceptional Moufang quadrangles of type F4

Koen Struyve

Type: Article

Publication Date: 2009-01-01

Citations: 1

DOI: https://doi.org/10.2140/iig.2009.10.121

Abstract

Departing from a Moufang set related to a polarity in an exceptional Moufang quadrangle of type F 4 , 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 F 4 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 n-gons with n ≥ 3.

Locations

Innovations in incidence geometry - View - PDF
Project Euclid (Cornell University) - View - PDF

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