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The Structure of Spherical Buildings - Richard M. Weiss

The Structure of Spherical Buildings

Hardcover

Published: 5th January 2004
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This book provides a clear and authoritative introduction to the theory of buildings, a topic of central importance to mathematicians interested in the geometric aspects of group theory. Its detailed presentation makes it suitable for graduate students as well as specialists. Richard Weiss begins with an introduction to Coxeter groups and goes on to present basic properties of arbitrary buildings before specializing to the spherical case. Buildings are described throughout in the language of graph theory.

"The Structure of Spherical Buildings" includes a reworking of the proof of Jacques Tits's Theorem 4.1.2. upon which Tits's classification of thick irreducible spherical buildings of rank at least three is based. In fact, this is the first book to include a proof of this famous result since its original publication. Theorem 4.1.2 is followed by a systematic study of the structure of spherical buildings and their automorphism groups based on the Moufang property. Moufang buildings of rank two were recently classified by Tits and Weiss. The last chapter provides an overview of the classification of spherical buildings, one that reflects these and other important developments.

"Richard M. Weiss's book is an extremely valuable addition to the literature."--Kenneth S. Brown, Bulletin of the American Mathematical Society

Prefacep. ix
Chamber Systemsp. 1
Coxeter Groupsp. 9
Rootsp. 17
Reduced Wordsp. 27
Oppositesp. 33
2-Interiorsp. 41
Buildingsp. 47
Apartmentsp. 61
Spherical Buildingsp. 73
Extensions of Isometriesp. 81
The Moufang Propertyp. 91
Root Group Labelingsp. 117
Referencesp. 131
Indexp. 133
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780691117331
ISBN-10: 0691117330
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 144
Published: 5th January 2004
Country of Publication: US
Dimensions (cm): 24.49 x 15.75  x 1.75
Weight (kg): 0.39