The Structure of Affine Buildings. (AM-168) / / Richard M. Weiss.

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: Weiss, Richard M.,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2008]; ©2009
• Year of Publication: 2008
• Edition: Course Book
• Language: English
• Series: Annals of Mathematics Studies ; 168
• Physical Description: 1 online resource (384 p.) :; 8 line illus. 8 tables.
• Other title: Frontmatter --; 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 E6, E7 and E8 --; 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
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9781400829057; 9783110494914; 9783110442502
• DOI: 10.1515/9781400829057
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Richard M. Weiss.

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.