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Descent in Buildings (AM-190)$
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Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss

Print publication date: 2015

Print ISBN-13: 9780691166902

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691166902.001.0001

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Moufang Structures

Moufang Structures

Chapter:
(p.205) Chapter Twenty Four Moufang Structures
Source:
Descent in Buildings (AM-190)
Author(s):

Bernhard M¨uhlherr

Holger P. Petersson

Richard M. Weiss

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691166902.003.0024

This chapter uses the notion of a Moufang structure to show that if Δ‎ is a spherical building satisfying the Moufang condition and Γ‎ is a descent group of Δ‎, then the fixed point building Δ‎Γ‎ also satisfies the Moufang condition. The discussion begins with the notation: Let (W, S) denote the type of Δ‎, let G = Aut(Δ‎) and let G° denote the group of type-preserving elements of G. The chapter then presents the conditions for an element g of G to be unipotent and for a subgroup U of G to be unipotent. It also describes a unipotent group U stabilizing a residue R and a unipotent element fixing two chambers x and y. Finally, it considers the set of extensions that forms a group acting faithfully on R.

Keywords:   spherical building, Moufang structure, Moufang condition, descent group, fixed point building, unipotent group, residue, chamber

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