The Structure of Affine Buildings

by Richard M. Weiss

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:	9781400829057
Publisher:	Princeton University Press
Publication date:	09/08/2008
Series:	Annals of Mathematics Studies , #168
Sold by:	Barnes & Noble
Format:	eBook
Pages:	384
File size:	3 MB

About the Author

Richard M. Weiss is the William Walker Professor of Mathematics at Tufts University and Honorary Professor in the School of Mathematics and Statistics at the University of Birmingham in the United Kingdom. He is the author of The Structure of Spherical Buildings and Quadrangular Algebras (both Princeton) and the coauthor with
Jacques Tits of Moufang Polygons. He received a Humboldt Research Prize in 2004.

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