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Classification of pseudo-reductive groups / / Brian Conrad, Gopal Prasad
Classification of pseudo-reductive groups / / Brian Conrad, Gopal Prasad
Autore Conrad Brian <1970->
Pubbl/distr/stampa Princeton, New Jersey ; ; Oxford, England : , : Princeton University Press, , 2016
Descrizione fisica 1 online resource (256 p.)
Disciplina 512/.55
Collana Annals of Mathematics Studies
Soggetto topico Linear algebraic groups
Group theory
Geometry, Algebraic
Soggetto non controllato "ient homomorphism
Cartan k-subgroup
Dynkin diagram
Isogeny Theorem
Isomorphism Theorem
Levi subgroup
SeveriЂrauer variety
Tits classification
Tits-style classification
Weil restriction
algebraic geometry
automorphism functor
automorphism scheme
automorphism
canonical central extensions
central "ient
central extension
characteristic 2.
conformal isometry
degenerate quadratic form
double bond
exotic construction
field-theoretic invariant
generalized exotic group
generalized standard group
generalized standard presentation
generalized standard
isomorphism class
isomorphism
isotropic group
k-tame central extension
linear isomorphism
linear-algebraic invariant
maximal torus
minimal type
non-reduced root system
number theory
pseudo-isogeny
pseudo-reductive group
pseudo-semisimple group
pseudo-simple group
pseudo-simple k-group
pseudo-split form
pseudo-split
quadratic space
quadrics
rank-1
rank-2
rigidity property
root field
root system
scheme-theoretic center
semisimple "ient
semisimple k-group
structure theorem
ISBN 1-4008-7402-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Front matter -- Contents -- 1. Introduction -- 2. Preliminary notions -- 3. Field-theoretic and linear-algebraic invariants -- 4. Central extensions and groups locally of minimal type -- 5. Universal smooth k-tame central extension -- 6. Automorphisms, isomorphisms, and Tits classification -- 7. Constructions with regular degenerate quadratic forms -- 8. Constructions when Φ has a double bond -- 9. Generalization of the standard construction -- A. Pseudo-isogenies -- B. Clifford constructions -- C. Pseudo-split and quasi-split forms -- D. Basic exotic groups of type F4 of relative rank 2 -- Bibliography -- Index
Record Nr. UNINA-9910797511403321
Conrad Brian <1970->  
Princeton, New Jersey ; ; Oxford, England : , : Princeton University Press, , 2016
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Classification of pseudo-reductive groups / / Brian Conrad, Gopal Prasad
Classification of pseudo-reductive groups / / Brian Conrad, Gopal Prasad
Autore Conrad Brian <1970->
Pubbl/distr/stampa Princeton, New Jersey ; ; Oxford, England : , : Princeton University Press, , 2016
Descrizione fisica 1 online resource (256 p.)
Disciplina 512/.55
Collana Annals of Mathematics Studies
Soggetto topico Linear algebraic groups
Group theory
Geometry, Algebraic
Soggetto non controllato "ient homomorphism
Cartan k-subgroup
Dynkin diagram
Isogeny Theorem
Isomorphism Theorem
Levi subgroup
SeveriЂrauer variety
Tits classification
Tits-style classification
Weil restriction
algebraic geometry
automorphism functor
automorphism scheme
automorphism
canonical central extensions
central "ient
central extension
characteristic 2.
conformal isometry
degenerate quadratic form
double bond
exotic construction
field-theoretic invariant
generalized exotic group
generalized standard group
generalized standard presentation
generalized standard
isomorphism class
isomorphism
isotropic group
k-tame central extension
linear isomorphism
linear-algebraic invariant
maximal torus
minimal type
non-reduced root system
number theory
pseudo-isogeny
pseudo-reductive group
pseudo-semisimple group
pseudo-simple group
pseudo-simple k-group
pseudo-split form
pseudo-split
quadratic space
quadrics
rank-1
rank-2
rigidity property
root field
root system
scheme-theoretic center
semisimple "ient
semisimple k-group
structure theorem
ISBN 1-4008-7402-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Front matter -- Contents -- 1. Introduction -- 2. Preliminary notions -- 3. Field-theoretic and linear-algebraic invariants -- 4. Central extensions and groups locally of minimal type -- 5. Universal smooth k-tame central extension -- 6. Automorphisms, isomorphisms, and Tits classification -- 7. Constructions with regular degenerate quadratic forms -- 8. Constructions when Φ has a double bond -- 9. Generalization of the standard construction -- A. Pseudo-isogenies -- B. Clifford constructions -- C. Pseudo-split and quasi-split forms -- D. Basic exotic groups of type F4 of relative rank 2 -- Bibliography -- Index
Record Nr. UNINA-9910813208303321
Conrad Brian <1970->  
Princeton, New Jersey ; ; Oxford, England : , : Princeton University Press, , 2016
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Descent in buildings / / Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss
Descent in buildings / / Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss
Autore Mühlherr Bernhard Matthias
Pubbl/distr/stampa Princeton : , : Princeton University Press, , 2015
Descrizione fisica 1 online resource (353 pages) : illustrations
Disciplina 516/.13
Collana Annals of mathematics studies
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
ISBN 1-4008-7401-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
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
Record Nr. UNINA-9910797524903321
Mühlherr Bernhard Matthias  
Princeton : , : Princeton University Press, , 2015
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Descent in buildings / / Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss
Descent in buildings / / Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss
Autore Mühlherr Bernhard Matthias
Pubbl/distr/stampa Princeton : , : Princeton University Press, , 2015
Descrizione fisica 1 online resource (353 pages) : illustrations
Disciplina 516/.13
Collana Annals of mathematics studies
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
ISBN 1-4008-7401-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
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
Record Nr. UNINA-9910822250603321
Mühlherr Bernhard Matthias  
Princeton : , : Princeton University Press, , 2015
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui