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



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Autore: Mühlherr Bernhard Matthias Visualizza persona
Titolo: Descent in buildings / / Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss Visualizza cluster
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  Visualizza cluster
ISBN: 1-4008-7401-7
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910797524903321
Lo trovi qui: Univ. Federico II
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Serie: Annals of mathematics studies ; ; 190.