The Structure of Affine Buildings. (AM-168) (Annals of Mathematics Studies)

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 Chapter 1. Affine Coxeter Diagrams Chapter 2. Root Systems Chapter 3. Root Data with Valuation Chapter 4. Sectors Chapter 5. Faces Chapter 6. Gems Chapter 7. Affine Buildings Chapter 8. The Building at Infinity Chapter 9. Trees with Valuation Chapter 10. Wall Trees Chapter 11. Panel Trees Chapter 12. Tree-Preserving Isomorphisms Chapter 13. The Moufang Property at Infinity Chapter 14. Existence Chapter 15. Partial Valuations Chapter 16. Bruhat-Tits Theory Chapter 17. Completions Chapter 18. Automorphisms and Residues Chapter 19. Quadrangles of Quadratic Form Type Chapter 20. Quadrangles of Indifferent Type Chapter 21. Quadrangles of Type E 6 , E 7 and E 8 Chapter 22. Quadrangles of Type F4 Chapter 23. Quadrangles of Involutory Type Chapter 24. Pseudo-Quadratic Quadrangles Chapter 25. Hexagons Chapter 26. Assorted Conclusions Chapter 27. Summary of the Classification Chapter 28. Locally Finite Bruhat-Tits Buildings Chapter 29. Appendix A Chapter 30. Appendix B Bibliography Index 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 .