The structure of affine buildings [[electronic resource] /] / Richard M. Weiss

• Autore: Weiss Richard M (Richard Mark), <1946->
• Pubblicazione: Princeton, N.J., : Princeton University Press, c2009
• Edizione: Course Book
• Descrizione fisica: 1 online resource (381 p.)
• Disciplina: 512/.2
• Soggetto topico: Buildings (Group theory); Moufang loops; Automorphisms; Affine algebraic groups
• Soggetto non controllato: Addition; Additive group; Additive inverse; Algebraic group; Algebraic structure; Ambient space; Associative property; Automorphism; Big O notation; Bijection; Bilinear form; Bounded set (topological vector space); Bounded set; Calculation; Cardinality; Cauchy sequence; Commutative property; Complete graph; Complete metric space; Composition algebra; Connected component (graph theory); Consistency; Continuous function; Coordinate system; Corollary; Coxeter group; Coxeter–Dynkin diagram; Diagram (category theory); Diameter; Dimension; Discrete valuation; Division algebra; Dot product; Dynkin diagram; E6 (mathematics); E7 (mathematics); E8 (mathematics); Empty set; Equipollence (geometry); Equivalence class; Equivalence relation; Euclidean geometry; Euclidean space; Existential quantification; Free monoid; Fundamental domain; Hyperplane; Infimum and supremum; Jacques Tits; K0; Linear combination; Mathematical induction; Metric space; Multiple edges; Multiplicative inverse; Number theory; Octonion; Parameter; Permutation group; Permutation; Pointwise; Polygon; Projective line; Quadratic form; Quaternion; Remainder; Root datum; Root system; Scientific notation; Sphere; Subgroup; Subring; Subset; Substructure; Theorem; Topology of uniform convergence; Topology; Torus; Tree (data structure); Tree structure; Two-dimensional space; Uniform continuity; Valuation (algebra); Vector space; Without loss of generality
• Classificazione: SI 830
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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
• Sommario/riassunto: 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.
• Titolo autorizzato: The structure of affine buildings
• ISBN: 1-282-45836-1; 9786612458361; 1-4008-2905-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910828976703321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; no. 168.