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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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Pseudo-Split Buildings

Pseudo-Split Buildings

(p.243) Chapter Twenty Eight Pseudo-Split Buildings
Descent in Buildings (AM-190)

Bernhard M¨uhlherr

Holger P. Petersson

Richard M. Weiss

Princeton University Press

This chapter introduces a class of Moufang spherical buildings known as pseudo-split buildings and considers the notion of the field of definition of a spherical building satisfying the Moufang condition. It begins with the notation: Let Δ‎ be an irreducible spherical building satisfying the Moufang condition, and let ℓ denote its rank (so ℓ is greater than or equal to 2 by definition). It then characterizes pseudo-split buildings as the spherical buildings which can be embedded in a split building of the same type. It also presents the proposition stating that every pseudo-split building is a subbuilding of a split building.

Keywords:   pseudo-split building, Moufang spherical building, spherical building, Moufang condition, split building, subbuilding

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