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The Structure of Spherical Buildings
     

The Structure of Spherical Buildings

by Richard M. Weiss
 

ISBN-10: 0691117330

ISBN-13: 9780691117331

Pub. Date: 01/05/2004

Publisher: Princeton University Press

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

Overview

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.

Product Details

ISBN-13:
9780691117331
Publisher:
Princeton University Press
Publication date:
01/05/2004
Edition description:
New Edition
Pages:
160
Product dimensions:
6.20(w) x 9.64(h) x 0.69(d)

Table of Contents


Preface ix
Chapter 1. Chamber Systems 1
Chapter 2. Coxeter Groups 9
Chapter 3. Roots 17
Chapter 4. Reduced Words 27
Chapter 5. Opposites 33
Chapter 6. 2-Interiors 41
Chapter 7. Buildings 47
Chapter 8. Apartments 61
Chapter 9. Spherical Buildings 73
Chapter 10. Extensions of Isometries 81
Chapter 11. The Moufang Property 91
Chapter 12. Root Group Labelings 117
References 131
Index 133

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