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基本説明
A detailed presentation of the complete proof of the classification of Bruhat-Tits buildings first completed by Jacques Tits in 1986.
Full Description
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.
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
