ISBN-10:
0691117330
ISBN-13:
9780691117331
Pub. Date:
01/25/2004
Publisher:
Princeton University Press
The Structure of Spherical Buildings

The Structure of Spherical Buildings

by Richard M. Weiss

Hardcover

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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: 01/25/2004
Edition description: New Edition
Pages: 144
Product dimensions: 6.10(w) x 9.20(h) x 0.70(d)

About the Author

Richard M. Weiss is William Walker Professor at Tufts University. He is the coauthor, with Jacques Tits, of Moufang Polygons.

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

What People are Saying About This

Hendrik Van Maldeghem

This is the best currently available introduction to the theory of buildings. And it brings the reader to a very important theorem in the theory of spherical buildings. Moreover, it is very carefully written: obviously the author spent quite some time arranging the different results in the right order, which isn't a straightforward task. As for explaining the really hard part of the classification of spherical buildings, this book is a perfect complement to the existing literature.
Hendrik Van Maldeghem, Ghent University

Ronan

This book makes an important contribution to the theory of buildings, developing some material in ways that were unavailable until recently. Weiss is an expert in the field who has produced a book that will be useful to anyone learning the subject.
Mark A. Ronan, University of Illinois at Chicago and University College London

From the Publisher

"This book makes an important contribution to the theory of buildings, developing some material in ways that were unavailable until recently. Weiss is an expert in the field who has produced a book that will be useful to anyone learning the subject."—Mark A. Ronan, University of Illinois at Chicago and University College London

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