TY  - BOOK
AU  - Weiss,Richard M.
TI  - The Structure of Spherical Buildings
SN  - 9780691216041
AV  - QA179 .W45 2003eb
U1  - 512/.2 22
PY  - 2021///]
CY  - Princeton, NJ : 
PB  - Princeton University Press, 
KW  - Buildings (Group theory)
KW  - BUSINESS & ECONOMICS / Economics / Macroeconomics
KW  - bisacsh
KW  - BN-pair
KW  - Tits system
KW  - Weyl distance
KW  - Weyl group
KW  - adjacent
KW  - bipartite
KW  - building
KW  - complex
KW  - concatenation
KW  - deletion
KW  - edge coloring
KW  - endomorphism
KW  - folding
KW  - free group
KW  - gallery
KW  - girth
KW  - graph
KW  - insertion
KW  - involution
KW  - isometry
KW  - multiple edge
KW  - octonion division algebra
KW  - panel
KW  - path
KW  - pre-gallery
KW  - realizable
KW  - regular group action
KW  - root group
KW  - skew-hermitian form
KW  - sub-chamber system
KW  - subbuilding
N1  - 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
N2  - 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
UR  - https://doi.org/10.1515/9780691216041?locatt=mode:legacy
UR  - https://www.degruyter.com/isbn/9780691216041
UR  - https://www.degruyter.com/cover/covers/9780691216041.jpg
ER  -