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book: The Structure of Spherical Buildings
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The Structure of Spherical Buildings

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Language: English
Published/Copyright: 2020

About this book

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.

Author / Editor information

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

Reviews

"Richard M. Weiss's book is an extremely valuable addition to the literature."---Kenneth S. Brown, Bulletin of the American Mathematical Society

Topics

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    Frontmatter

    i
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    Contents

    vii
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    Preface

    ix
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    Chapter 1. Chamber Systems

    1
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    Chapter 2. Coxeter Groups

    9
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    Chapter 3. Roots

    17
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    Chapter 4. Reduced Words

    27
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    Chapter 5. Opposites

    33
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    Chapter 6. 2-lnteriors

    41
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    Chapter 7. Buildings

    47
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    Chapter 8. Apartments

    61
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    Chapter 9. Spherical Buildings

    73
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    Chapter 10. Extensions of Isometries

    81
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    Chapter 11. The Moufang Property

    91
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    Chapter 12. Root Group Labelings

    117
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    References

    131
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    Index

    133
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Publishing information
Pages and Images/Illustrations in book
eBook published on:
March 24, 2021
eBook ISBN:
9780691216041
Pages and Images/Illustrations in book
View content
https://doi.org/10.1515/9780691216041
eBook ISBN: 9780691216041
Keywords for this book
Subset; Theorem; Edge coloring; Diameter; Coxeter group; Bipartite graph; Homotopy; Existential quantification; Sphere; Automorphism; Subgroup; Convex set; Complete bipartite graph; Tetrahedron; Polygon; Complete graph; Euclidean space; Infimum and supremum; Simplicial complex; Special case; Equivalence relation; Sequence; Monoid; System U; Free monoid; Additive group; Incidence geometry; Bijection; Big O notation; Equivalence class; Direct product; Conjugacy class; Normal subgroup; Cardinality; Frattini subgroup; Pointwise; Mathematical induction; Finite group; Homomorphism; Quotient group; Nilpotent group; Realizability; Commutator; Free group; Calculation; Disjoint sets; Function composition; Scientific notation; Finite set; Simple group; Endomorphism; Group theory; Mathematics; Jacques Tits; Explicit formulae (L-function); Three-dimensional space (mathematics); Empty set; Vector space; Disjoint union; Corollary; Irreducibility (mathematics); Lie group; Fundamental theorem; Weyl group; Permutation; Girth (graph theory); Graph automorphism; Diagram (category theory); Cayley graph; Algebraic group
Audience(s) for this book
For an expert adult audience, including professional development and academic research
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