Jump to ContentJump to Main Navigation
Descent in Buildings (AM-190)$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in HSO for personal use (for details see www.princeton.universitypressscholarship.com/page/privacy-policy).date: 16 December 2018

Buildings

Buildings

Chapter:
(p.3) Chapter One Buildings
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/9780691166902.003.0001

This chapter assembles a few standard definitions, fixes some notation, and reviews a few of the results about buildings and Moufang polygons. It also summarizes the basic facts about Coxeter groups and buildings, including the fundamental properties of roots, residues, apartments, and projection maps. The chapter defines a Moufang building as spherical, thick, irreducible and of rank at least 2, and a Bruhat-Tits building as a thick irreducible affine building whose building at infinity is Moufang. Furthermore, it presents a fundamental result of Tits: that an irreducible thick spherical building of rank at least 3 satisfies the Moufang condition as do all the irreducible residues of rank at least 2 of such a building. Finally, it considers a simplicial complex, the dimension of which is its cardinality minus one.

Keywords:   building, Moufang polygon, Coxeter group, root, residue, projection map, Moufang building, Bruhat-Tits building, spherical building, simplicial complex

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.