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Groupes algébriques semi-simples en dimension cohomologique ≤2 [[electronic resource] ] : Semisimple algebraic groups in cohomological dimension ≤2 / / by Philippe Gille
| Groupes algébriques semi-simples en dimension cohomologique ≤2 [[electronic resource] ] : Semisimple algebraic groups in cohomological dimension ≤2 / / by Philippe Gille |
| Autore | Gille Philippe <1968-> |
| Edizione | [1st ed. 2019.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 |
| Descrizione fisica | 1 online resource (XXII, 169 p.) |
| Disciplina | 512.2 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Group theory
Universal algebra Group Theory and Generalizations General Algebraic Systems |
| ISBN | 3-030-17272-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | fre |
| Nota di contenuto | Préface -- 1 Généralités -- 2 Groupes réductifs -- 3 Sous-groupes des groupes algébriques, déploiement -- 4 Dimension cohomologique séparable -- 5 Tores algébriques, Conjecture I et groupes de normes -- 6 Conjecture II, le cas quasi–déployé -- 7 Groupes classiques -- 8 Groupes exceptionnels -- 9 Applications -- Appendice : Indices de Tits -- Bibliographie -- Index. |
| Record Nr. | UNISA-996466645103316 |
Gille Philippe <1968->
|
||
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Groupes algébriques semi-simples en dimension cohomologique ≤2 [[electronic resource] ] : Semisimple algebraic groups in cohomological dimension ≤2 / / by Philippe Gille
| Groupes algébriques semi-simples en dimension cohomologique ≤2 [[electronic resource] ] : Semisimple algebraic groups in cohomological dimension ≤2 / / by Philippe Gille |
| Autore | Gille Philippe <1968-> |
| Edizione | [1st ed. 2019.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 |
| Descrizione fisica | 1 online resource (XXII, 169 p.) |
| Disciplina | 512.2 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Group theory
Universal algebra Group Theory and Generalizations General Algebraic Systems |
| ISBN | 3-030-17272-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | fre |
| Nota di contenuto | Préface -- 1 Généralités -- 2 Groupes réductifs -- 3 Sous-groupes des groupes algébriques, déploiement -- 4 Dimension cohomologique séparable -- 5 Tores algébriques, Conjecture I et groupes de normes -- 6 Conjecture II, le cas quasi–déployé -- 7 Groupes classiques -- 8 Groupes exceptionnels -- 9 Applications -- Appendice : Indices de Tits -- Bibliographie -- Index. |
| Record Nr. | UNINA-9910392720403321 |
|
Gille Philippe <1968->
|
||
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Torsors, reductive group schemes and extended affine lie algebras / / Philippe Gille, Arturo Pianzola
| Torsors, reductive group schemes and extended affine lie algebras / / Philippe Gille, Arturo Pianzola |
| Autore | Gille Philippe <1968-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (124 p.) |
| Disciplina | 512/.482 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Kac-Moody algebras
Linear algebraic groups Geometry, Algebraic |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-1063-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Generalities on the algebraic fundamental group, torsors, and reductive group schemes""; ""2.1. The fundamental group""; ""2.2. Torsors""; ""2.3. An example: Laurent polynomials in characteristic 0""; ""2.4. Reductive group schemes: Irreducibility and isotropy""; ""Chapter 3. Loop, finite and toral torsors""; ""3.1. Loop torsors""; ""3.2. Loop reductive groups""; ""3.3. Loop torsors at a rational base point""; ""3.4. Finite torsors""; ""3.5. Toral torsors""; ""Chapter 4. Semilinear considerations""; ""4.1. Semilinear morphisms""
""4.2. Semilinear morphisms""""4.3. Case of affine schemes""; ""4.4. Group functors""; ""4.5. Semilinear version of a theorem of Borel-Mostow""; ""4.6. Existence of maximal tori in loop groups""; ""4.7. Variations of a result of Sansuc""; ""Chapter 5. Maximal tori of group schemes over the punctured line""; ""5.1. Twin buildings""; ""5.2. Proof of Theorem 5.1""; ""Chapter 6. Internal characterization of loop torsors and applications""; ""6.1. Internal characterization of loop torsors""; ""6.2. Applications to (algebraic) Laurent series""; ""Chapter 7. Isotropy of loop torsors"" ""7.1. Fixed point statements""""7.2. Case of flag varieties""; ""7.3. Anisotropic loop torsors""; ""Chapter 8. Acyclicity""; ""8.1. The proof""; ""8.2. Application: Witt-Tits decomposition""; ""8.3. Classification of semisimple â€?loop adjoint groups""; ""8.4. Action of _{ }(â??)""; ""Chapter 9. Small dimensions""; ""9.1. The one-dimensional case""; ""9.2. The two-dimensional case""; ""Chapter 10. The case of orthogonal groups""; ""Chapter 11. Groups of type â??""; ""Chapter 12. Case of groups of type â??, â?? and simply connected â?? in nullity 3"" ""Chapter 13. The case of _{ }""""13.1. Loop Azumaya algebras""; ""13.2. The one-dimensional case""; ""13.3. The geometric case""; ""13.4. Loop algebras of inner type ""; ""Chapter 14. Invariants attached to EALAs and multiloop algebras""; ""Chapter 15. Appendix 1: Pseudo-parabolic subgroup schemes""; ""15.1. The case of _{ ,â??}""; ""15.2. The general case""; ""Chapter 16. Appendix 2: Global automorphisms of â€?torsors over the projective line""; ""Bibliography"" |
| Record Nr. | UNINA-9910480392803321 |
|
Gille Philippe <1968->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Torsors, reductive group schemes and extended affine lie algebras / / Philippe Gille, Arturo Pianzola
| Torsors, reductive group schemes and extended affine lie algebras / / Philippe Gille, Arturo Pianzola |
| Autore | Gille Philippe <1968-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (124 p.) |
| Disciplina | 512/.482 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Kac-Moody algebras
Linear algebraic groups Geometry, Algebraic |
| ISBN | 1-4704-1063-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Generalities on the algebraic fundamental group, torsors, and reductive group schemes""; ""2.1. The fundamental group""; ""2.2. Torsors""; ""2.3. An example: Laurent polynomials in characteristic 0""; ""2.4. Reductive group schemes: Irreducibility and isotropy""; ""Chapter 3. Loop, finite and toral torsors""; ""3.1. Loop torsors""; ""3.2. Loop reductive groups""; ""3.3. Loop torsors at a rational base point""; ""3.4. Finite torsors""; ""3.5. Toral torsors""; ""Chapter 4. Semilinear considerations""; ""4.1. Semilinear morphisms""
""4.2. Semilinear morphisms""""4.3. Case of affine schemes""; ""4.4. Group functors""; ""4.5. Semilinear version of a theorem of Borel-Mostow""; ""4.6. Existence of maximal tori in loop groups""; ""4.7. Variations of a result of Sansuc""; ""Chapter 5. Maximal tori of group schemes over the punctured line""; ""5.1. Twin buildings""; ""5.2. Proof of Theorem 5.1""; ""Chapter 6. Internal characterization of loop torsors and applications""; ""6.1. Internal characterization of loop torsors""; ""6.2. Applications to (algebraic) Laurent series""; ""Chapter 7. Isotropy of loop torsors"" ""7.1. Fixed point statements""""7.2. Case of flag varieties""; ""7.3. Anisotropic loop torsors""; ""Chapter 8. Acyclicity""; ""8.1. The proof""; ""8.2. Application: Witt-Tits decomposition""; ""8.3. Classification of semisimple â€?loop adjoint groups""; ""8.4. Action of _{ }(â??)""; ""Chapter 9. Small dimensions""; ""9.1. The one-dimensional case""; ""9.2. The two-dimensional case""; ""Chapter 10. The case of orthogonal groups""; ""Chapter 11. Groups of type â??""; ""Chapter 12. Case of groups of type â??, â?? and simply connected â?? in nullity 3"" ""Chapter 13. The case of _{ }""""13.1. Loop Azumaya algebras""; ""13.2. The one-dimensional case""; ""13.3. The geometric case""; ""13.4. Loop algebras of inner type ""; ""Chapter 14. Invariants attached to EALAs and multiloop algebras""; ""Chapter 15. Appendix 1: Pseudo-parabolic subgroup schemes""; ""15.1. The case of _{ ,â??}""; ""15.2. The general case""; ""Chapter 16. Appendix 2: Global automorphisms of â€?torsors over the projective line""; ""Bibliography"" |
| Record Nr. | UNINA-9910796030803321 |
|
Gille Philippe <1968->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Torsors, reductive group schemes and extended affine lie algebras / / Philippe Gille, Arturo Pianzola
| Torsors, reductive group schemes and extended affine lie algebras / / Philippe Gille, Arturo Pianzola |
| Autore | Gille Philippe <1968-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (124 p.) |
| Disciplina | 512/.482 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Kac-Moody algebras
Linear algebraic groups Geometry, Algebraic |
| ISBN | 1-4704-1063-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Generalities on the algebraic fundamental group, torsors, and reductive group schemes""; ""2.1. The fundamental group""; ""2.2. Torsors""; ""2.3. An example: Laurent polynomials in characteristic 0""; ""2.4. Reductive group schemes: Irreducibility and isotropy""; ""Chapter 3. Loop, finite and toral torsors""; ""3.1. Loop torsors""; ""3.2. Loop reductive groups""; ""3.3. Loop torsors at a rational base point""; ""3.4. Finite torsors""; ""3.5. Toral torsors""; ""Chapter 4. Semilinear considerations""; ""4.1. Semilinear morphisms""
""4.2. Semilinear morphisms""""4.3. Case of affine schemes""; ""4.4. Group functors""; ""4.5. Semilinear version of a theorem of Borel-Mostow""; ""4.6. Existence of maximal tori in loop groups""; ""4.7. Variations of a result of Sansuc""; ""Chapter 5. Maximal tori of group schemes over the punctured line""; ""5.1. Twin buildings""; ""5.2. Proof of Theorem 5.1""; ""Chapter 6. Internal characterization of loop torsors and applications""; ""6.1. Internal characterization of loop torsors""; ""6.2. Applications to (algebraic) Laurent series""; ""Chapter 7. Isotropy of loop torsors"" ""7.1. Fixed point statements""""7.2. Case of flag varieties""; ""7.3. Anisotropic loop torsors""; ""Chapter 8. Acyclicity""; ""8.1. The proof""; ""8.2. Application: Witt-Tits decomposition""; ""8.3. Classification of semisimple â€?loop adjoint groups""; ""8.4. Action of _{ }(â??)""; ""Chapter 9. Small dimensions""; ""9.1. The one-dimensional case""; ""9.2. The two-dimensional case""; ""Chapter 10. The case of orthogonal groups""; ""Chapter 11. Groups of type â??""; ""Chapter 12. Case of groups of type â??, â?? and simply connected â?? in nullity 3"" ""Chapter 13. The case of _{ }""""13.1. Loop Azumaya algebras""; ""13.2. The one-dimensional case""; ""13.3. The geometric case""; ""13.4. Loop algebras of inner type ""; ""Chapter 14. Invariants attached to EALAs and multiloop algebras""; ""Chapter 15. Appendix 1: Pseudo-parabolic subgroup schemes""; ""15.1. The case of _{ ,â??}""; ""15.2. The general case""; ""Chapter 16. Appendix 2: Global automorphisms of â€?torsors over the projective line""; ""Bibliography"" |
| Record Nr. | UNINA-9910819072103321 |
|
Gille Philippe <1968->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||