04171nam 2200613 450 991048039280332120170822144401.01-4704-1063-X(CKB)3780000000000327(EBL)3114045(SSID)ssj0001034809(PQKBManifestationID)11562942(PQKBTitleCode)TC0001034809(PQKBWorkID)11015565(PQKB)11443135(MiAaPQ)EBC3114045(PPN)195408470(EXLCZ)99378000000000032720150415h20132013 uy 0engur|n|---|||||txtccrTorsors, reductive group schemes and extended affine lie algebras /Philippe Gille, Arturo PianzolaProvidence, Rhode Island :American Mathematical Society,2013.©20131 online resource (124 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 226, Number 1063"Volume 226, Number 1063 (fourth of 5 numbers)."0-8218-8774-2 Includes bibliographical references.""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""Memoirs of the American Mathematical Society ;Volume 226, Number 1063.Kac-Moody algebrasLinear algebraic groupsGeometry, AlgebraicElectronic books.Kac-Moody algebras.Linear algebraic groups.Geometry, Algebraic.512/.482Gille Philippe1968-938069Pianzola Arturo1955-MiAaPQMiAaPQMiAaPQBOOK9910480392803321Torsors, reductive group schemes and extended affine lie algebras2113240UNINA