Tits endomorphisms and buildings of type F4

Tom De Medts, Yoav Segev, Richard M. Weiss

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The fixed point building of a polarity of a Moufang quadrangle of type F4 is a Moufang set, as is the fixed point building of a semi-linear automorphism of order 2 of a Moufang octagon that stabilizes at least two panels of one type but none of the other. We show that these two classes of Moufang sets are, in fact, the same, that each member of this class can be constructed as the fixed point building of a group of order 4 acting on a building of type F4 and that the group generated by all the root groups of any one of these Moufang sets is simple.

Original languageEnglish
Pages (from-to)2349-2421
Number of pages73
JournalAnnales de l'Institut Fourier
Volume67
Issue number6
DOIs
StatePublished - 1 Jan 2017

Keywords

  • Building
  • Descent
  • Moufang octagon
  • Moufang quadrangle
  • Moufang set
  • Polarity

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