The Structure of spherical buildings / Richard M. Weiss.

Format:

Book

Author/Creator:

Weiss, Richard M., author.

Language:

English

Subjects (All):

Mathematics.

Physical Description:

1 online resource (154 pages) : illustrations

Place of Publication:

Princeton, New Jersey : Princeton University Press, 2004.

Summary:

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.

Contents:

Frontmatter

Contents

Preface

Chapter 1. Chamber Systems

Chapter 2. Coxeter Groups

Chapter 3. Roots

Chapter 4. Reduced Words

Chapter 5. Opposites

Chapter 6. 2-lnteriors

Chapter 7. Buildings

Chapter 8. Apartments

Chapter 9. Spherical Buildings

Chapter 10. Extensions of Isometries

Chapter 11. The Moufang Property

Chapter 12. Root Group Labelings

References

Index

Notes:

Description based on print version record.

Includes index.

Includes bibliographical references.

ISBN:

9780691216041

0691216045

OCLC:

1248759739