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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 Polygons

Moufang Polygons

Chapter:
(p.23) Chapter Three Moufang Polygons
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/9780691166902.003.0003

This chapter introduces some basic facts about Moufang polygons and root group sequences. For each root group sequence Ω‎, there is a unique Moufang polygon Δ‎ such that Ω‎ is isomorphic to a root group sequence of Δ‎. The classification of Moufang n-gons states that, up to isomorphism, there are no other Moufang polygons. The chapter also considers the notion of an isomorphism of root group sequences and the notion of an anti-isomorphism of root group sequences. It concludes with an example involving a non-trivial anisotropic quadratic space and a generalized quadrangle with a root group sequence.

Keywords:   root group sequence, Moufang polygon, isomorphism, anti-isomorphism, anisotropic quadratic space, generalized quadrangle

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