Richard M. Weiss

The Structure of Spherical Buildings (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Verso
• Erscheinungstermin: 21. Juli 2020
• Englisch
• ISBN-13: 9780691216041
• Artikelnr.: 59636362

Autorenporträt

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

Inhaltsangabe

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