Descent in buildings / / Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss

• Autore: Mühlherr Bernhard Matthias
• Pubblicazione: Princeton : , : Princeton University Press, , 2015
• Descrizione fisica: 1 online resource (353 pages) : illustrations
• Disciplina: 516/.13
• Soggetto topico: Buildings (Group theory); Combinatorial geometry
• Soggetto non controllato: Bruhat-Tits building; Clifford invariant; Coxeter diagram; Coxeter group; Coxeter system; Euclidean plane; Fundamental Theorem of Descent; Moufang building; Moufang condition; Moufang polygon; Moufang quadrangle; Moufang set; Moufang structure; Pfister form; Structure Theorem; Tits index; abelian group; absolute Coxeter diagram; absolute Coxeter system; absolute rank; affine building; algebraic group; anisotropic pseudo-quadratic space; anisotropic quadratic space; anti-isomorphism; apartment; arctic region; automorphism; bilinear form; biquaternion division algebra; building; canonical isomorphism; chamber; compatible representation; descent group; descent; discrete valuation; exceptional Moufang quadrangle; exceptional quadrangle; finite dimension; fixed point building; fixed point theory; gem; generalized quadrangle; hyperbolic plane; hyperbolic quadratic module; hyperbolic quadratic space; involutory set; isomorphism; isotropic quadratic space; length function; non-abelian group; parallel residues; polar space; projection map; proper indifferent set; proper involutory set; pseudo-quadratic space; pseudo-split building; quadratic form; quadratic module; quadratic space; quaternion division algebra; ramified quadrangle; ramified quaternion division algebra; ramified separable quadratic extension; relative Coxeter diagram; relative Coxeter group; relative Coxeter system; relative rank; residual quadratic spaces; residue; root group sequence; root; round quadratic space; scalar multiplication; semi-ramified quadrangle; separable quadratic extension; simplicial complex; special vertex; spherical building; split quadratic space; standard involution; subbuilding of split type; subbuilding; tamely ramified division algebra; thick building; thin T-building; trace map; trace; unramified quadrangle; unramified quadratic space; unramified quaternion division algebra; unramified separable quadratic extension; vector space; vertex; weak isomorphism; wild quadratic space
• Persona (resp. second.): PeterssonHolger P. <1939->; WeissRichard M <1946-> (Richard Mark)
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Frontmatter -- Contents -- Preface -- PART 1. Moufang Quadrangles -- Chapter 1. Buildings -- Chapter 2. Quadratic Forms -- Chapter 3. Moufang Polygons -- Chapter 4. Moufang Quadrangles -- Chapter 5. Linked Tori, I -- Chapter 6. Linked Tori, II -- Chapter 7. Quadratic Forms over a Local Field -- Chapter 8. Quadratic Forms of Type E6, E7 and E8 -- Chapter 9. Quadratic Forms of Type F4 -- PART 2. Residues in Bruhat-Tits Buildings -- Chapter 10. Residues -- Chapter 11. Unramified Quadrangles of Type E6, E7 and E8 -- Chapter 12. Semi-ramified Quadrangles of Type E6, E7 and E8 -- Chapter 13. Ramified Quadrangles of Type E6, E7 and E8 -- Chapter 14. Quadrangles of Type E6, E7 and E8: Summary -- Chapter 15. Totally Wild Quadratic Forms of Type E7 -- Chapter 16. Existence -- Chapter 17. Quadrangles of Type F4 -- Chapter 18. The Other Bruhat-Tits Buildings -- PART 3. Descent -- Chapter 19. Coxeter Groups -- Chapter 20. Tits Indices -- Chapter 21. Parallel Residues -- Chapter 22. Fixed Point Buildings -- Chapter 23. Subbuildings -- Chapter 24. Moufang Structures -- Chapter 25. Fixed Apartments -- Chapter 26. The Standard Metric -- Chapter 27. Affine Fixed Point Buildings -- PART 4. Galois Involutions -- Chapter 28. Pseudo-Split Buildings -- Chapter 29. Linear Automorphisms -- Chapter 30. Strictly Semi-linear Automorphisms -- Chapter 31. Galois Involutions -- Chapter 32. Unramified Galois Involutions -- PART 5. Exceptional Tits Indices -- Chapter 33. Residually Pseudo-Split Buildings -- Chapter 34. Forms of Residually Pseudo-Split Buildings -- Chapter 35. Orthogonal Buildings -- Chapter 36. Indices for the Exceptional Bruhat-Tits Buildings -- Bibliography -- Index
• Sommario/riassunto: Descent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. The authors then put their algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving necessary and sufficient conditions for the residues fixed by a group to form a kind of subbuilding or "form" of the original building. At the center of this theory is the notion of a Tits index, a combinatorial version of the notion of an index in the relative theory of algebraic groups. These results are combined at the end to show that every exceptional Bruhat-Tits building arises as a form of a "residually pseudo-split" Bruhat-Tits building. The book concludes with a display of the Tits indices associated with each of these exceptional forms.This is the third and final volume of a trilogy that began with Richard Weiss' The Structure of Spherical Buildings and The Structure of Affine Buildings.
• Titolo autorizzato: Descent in buildings
• ISBN: 1-4008-7401-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910822250603321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; 190.