LEADER 04117nam 2200601 450 001 9910812439503321 005 20170822144326.0 010 $a1-4704-0530-X 035 $a(CKB)3360000000465108 035 $a(EBL)3114048 035 $a(SSID)ssj0000888757 035 $a(PQKBManifestationID)11566298 035 $a(PQKBTitleCode)TC0000888757 035 $a(PQKBWorkID)10866078 035 $a(PQKB)11132855 035 $a(MiAaPQ)EBC3114048 035 $a(RPAM)15511631 035 $a(PPN)195418131 035 $a(EXLCZ)993360000000465108 100 $a20150415h20092009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$a"Abstract" homomorphisms of split Kac-Moody groups /$fPierre-Emmanuel Caprace 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2009. 210 4$dİ2009 215 $a1 online resource (108 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 198, Number 924 300 $a"Volume 198, Number 924 (first of 6 numbers)." 311 $a0-8218-4258-7 320 $aIncludes bibliographical references and index. 327 $a""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"" 327 $a""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"" 327 $a""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"" 327 $a""Chapter 7. Homomorphisms of Kac-Moody groups to algebraic groups""""7.1. The non-linearity theorem""; ""7.2. A combinatorial characterization of affine Coxeter groups""; ""7.3. On infinite root systems""; ""7.4. Proof of the non-linearity theorem""; ""Chapter 8. Unitary forms of Kac-Moody groups""; ""8.1. Introduction""; ""8.2. Definitions""; ""8.3. Isomorphisms of unitary forms""; ""8.4. Non-linearity""; ""Bibliography""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""G""; ""H""; ""I""; ""K""; ""L""; ""M""; ""N""; ""O""; ""P""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 198, Number 924. 606 $aIsomorphisms (Mathematics) 606 $aAutomorphisms 606 $aKac-Moody algebras 615 0$aIsomorphisms (Mathematics) 615 0$aAutomorphisms. 615 0$aKac-Moody algebras. 676 $a511.3/26 700 $aCaprace$b Pierre-Emmanuel$f1981-$01661549 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910812439503321 996 $a"Abstract" homomorphisms of split Kac-Moody groups$94017540 997 $aUNINA