04117nam 2200601 450 991081243950332120170822144326.01-4704-0530-X(CKB)3360000000465108(EBL)3114048(SSID)ssj0000888757(PQKBManifestationID)11566298(PQKBTitleCode)TC0000888757(PQKBWorkID)10866078(PQKB)11132855(MiAaPQ)EBC3114048(RPAM)15511631(PPN)195418131(EXLCZ)99336000000046510820150415h20092009 uy 0engur|n|---|||||txtccr"Abstract" homomorphisms of split Kac-Moody groups /Pierre-Emmanuel CapraceProvidence, Rhode Island :American Mathematical Society,2009.©20091 online resource (108 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 198, Number 924"Volume 198, Number 924 (first of 6 numbers)."0-8218-4258-7 Includes bibliographical references and index.""Contents""; ""Introduction""; ""Acknowledgements""; ""Chapter 1. The objects: Kac-Moody groups, root data and Tits buildings""; ""1.1. Kac-Moody groups and Tits functors""; ""1.2. Root data""; ""1.3. Tits buildings""; ""1.4. Twin root data and twin buildings: a short dictionary""; ""Chapter 2. Basic tools from geometric group theory""; ""2.1. CAT(0) geometry""; ""2.2. Rigidity of algebraic-group-actions on trees""; ""Chapter 3. Kac-Moody groups and algebraic groups""; ""3.1. Bounded subgroups""; ""3.2. Adjoint representation of Tits functors""""3.3. A few facts from the theory of algebraic groups""""Chapter 4. Isomorphisms of Kac-Moody groups: an overview""; ""4.1. The isomorphism theorem""; ""4.2. Diagonalizable subgroups and their centralizers""; ""4.3. Completely reducible subgroups and their centralizers""; ""4.4. Basic recognition of the ground field""; ""4.5. Detecting rank one subgroups of Kac-Moody groups""; ""4.6. Images of diagonalizable subgroups under Kac-Moody group isomorphisms""; ""4.7. A technical auxiliary to the isomorphism theorem""; ""Chapter 5. Isomorphisms of Kac-Moody groups in characteristic zero""""5.1. Rigidity of SL[sub(2)](Q)-actions on CAT(0) polyhedral complexes""""5.2. Homomorphisms of Chevalley groups over Q to Kac-Moody groups""; ""5.3. Regularity of diagonalizable subgroups""; ""5.4. Proof of the isomorphism theorem""; ""Chapter 6. Isomorphisms of Kac-Moody groups in positive characteristic""; ""6.1. On bounded subgroups of Kac-Moody groups""; ""6.2. Homomorphisms of certain algebraic groups to Kac-Moody groups""; ""6.3. Images of certain small subgroups under Kac-Moody group isomorphisms""; ""6.4. Proof of the isomorphism theorem""""Chapter 7. Homomorphisms of Kac-Moody groups to algebraic groups""""7.1. The non-linearity theorem""; ""7.2. A combinatorial characterization of affine Coxeter groups""; ""7.3. On infinite root systems""; ""7.4. Proof of the non-linearity theorem""; ""Chapter 8. Unitary forms of Kac-Moody groups""; ""8.1. Introduction""; ""8.2. Definitions""; ""8.3. Isomorphisms of unitary forms""; ""8.4. Non-linearity""; ""Bibliography""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""G""; ""H""; ""I""; ""K""; ""L""; ""M""; ""N""; ""O""; ""P""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""Memoirs of the American Mathematical Society ;Volume 198, Number 924.Isomorphisms (Mathematics)AutomorphismsKac-Moody algebrasIsomorphisms (Mathematics)Automorphisms.Kac-Moody algebras.511.3/26Caprace Pierre-Emmanuel1981-1661549MiAaPQMiAaPQMiAaPQBOOK9910812439503321"Abstract" homomorphisms of split Kac-Moody groups4017540UNINA