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The Structure of Spherical Buildings / Richard M. Weiss.

By: Material type: TextTextPublisher: Princeton, NJ : Princeton University Press, [2021]Copyright date: ©2004Description: 1 online resource (144 p.) : 16 line illusContent type:
Media type:
Carrier type:
ISBN:
  • 9780691216041
Subject(s): DDC classification:
  • 512/.2 22
LOC classification:
  • QA179 .W45 2003eb
Other classification:
  • online - DeGruyter
Online resources:
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
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.
Holdings
Item type Current library Call number URL Status Notes Barcode
eBook eBook Biblioteca "Angelicum" Pont. Univ. S.Tommaso d'Aquino Nuvola online online - DeGruyter (Browse shelf(Opens below)) Online access Not for loan (Accesso limitato) Accesso per gli utenti autorizzati / Access for authorized users (dgr)9780691216041

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

restricted access online access with authorization star

http://purl.org/coar/access_right/c_16ec

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.

Mode of access: Internet via World Wide Web.

In English.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021)