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

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 . Content: 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. Abstract: Gives a presentation of the complete proof of the classification of Bruhat-Tits buildings first completed by Jacques Tits in 1986. This book includes numerous results about automorphisms, completions, and residues of these buildings. Read more... 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 clas. Read more...