The Structure of Affine Buildings. (AM-168)

The Structure of Affine Buildings. (AM-168)

by Richard M. Weiss
     
 

ISBN-10: 0691136599

ISBN-13: 9780691136592

Pub. Date: 09/08/2008

Publisher: Princeton University Press

In The Structure of Affine Buildings, Richard Weiss gives a detailed presentation of the complete proof of the classification of Bruhat-Tits buildings first completed by Jacques Tits in 1986. The book includes numerous results about automorphisms, completions, and residues of these buildings. It also includes tables correlating the results in the locally finite…  See more details below

Overview

In The Structure of Affine Buildings, Richard Weiss gives a detailed presentation of the complete proof of the classification of Bruhat-Tits buildings first completed by Jacques Tits in 1986. The book includes numerous results about automorphisms, completions, and residues of these buildings. It also includes tables correlating the results in the locally finite case with the results of Tits's classification of absolutely simple algebraic groups defined over a local field. A companion to Weiss's The Structure of Spherical Buildings, The Structure of Affine Buildings is organized around the classification of spherical buildings and their root data as it is carried out in Tits and Weiss's Moufang Polygons.

Product Details

ISBN-13:
9780691136592
Publisher:
Princeton University Press
Publication date:
09/08/2008
Series:
Annals of Mathematics Studies Series
Pages:
392
Product dimensions:
6.30(w) x 9.30(h) x 1.20(d)

Table of Contents

Preface vii

Chapter 1. Affine Coxeter Diagrams 1

Chapter 2. Root Systems 13

Chapter 3. Root Data with Valuation 25

Chapter 4. Sectors 39

Chapter 5. Faces 45

Chapter 6. Gems 53

Chapter 7. Affine Buildings 59

Chapter 8. The Building at Infinity 67

Chapter 9. Trees with Valuation 77

Chapter 10. Wall Trees 89

Chapter 11. Panel Trees 101

Chapter 12. Tree-Preserving Isomorphisms 107

Chapter 13. The Moufang Property at Infinity 119

Chapter 14. Existence 131

Chapter 15. Partial Valuations 147

Chapter 16. Bruhat-Tits Theory 159

Chapter 17. Completions 167

Chapter 18. Automorphisms and Residues 175

Chapter 19. Quadrangles of Quadratic Form Type 189

Chapter 20. Quadrangles of Indifferent Type 205

Chapter 21. Quadrangles of Type E6, E7 and E8 209

Chapter 22. Quadrangles of Type F4 221

Chapter 23. Quadrangles of Involutory Type 229

Chapter 24. Pseudo-Quadratic Quadrangles 239

Chapter 25. Hexagons 261

Chapter 26. Assorted Conclusions 275

Chapter 27. Summary of the Classification 289

Chapter 28. Locally Finite Bruhat-Tits Buildings 297

Chapter 29. Appendix A 321

Chapter 30. Appendix B 343

Bibliography 361

Index 365

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