LEADER 04326nam 2200649 450 001 9910812749903321 005 20180613001302.0 010 $a1-4704-0340-4 035 $a(CKB)3360000000464931 035 $a(EBL)3114353 035 $a(SSID)ssj0000910356 035 $a(PQKBManifestationID)11595670 035 $a(PQKBTitleCode)TC0000910356 035 $a(PQKBWorkID)10932140 035 $a(PQKB)10855152 035 $a(MiAaPQ)EBC3114353 035 $a(RPAM)12648088 035 $a(PPN)195416333 035 $a(EXLCZ)993360000000464931 100 $a20020117h20022002 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAlmost commuting elements in compact Lie groups /$fArmand Borel, Robert Friedman, John W. Morgan 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2002] 210 4$dİ2002 215 $a1 online resource (153 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 747 300 $a"Volume 157, number 747 (third of 5 numbers)." 311 $a0-8218-2792-8 320 $aIncludes bibliographical references. 327 $a""Contents""; ""Chapter 1. Introduction""; ""1.1. Preliminaries""; ""1.2. The case of commuting pairs in a simply connected group""; ""1.3. c-pairs""; ""1.4. Commuting triples""; ""1.5. C-triples""; ""1.6. Quotients of diagram automorphisms""; ""1.7. Description of S(k) and S[sup(I??c)](g,k)""; ""1.8. Chern-Simons invariants and Witten's ""Clockwise Symmetry Conjecture""""; ""1.9. Outline of the paper""; ""1.10. History""; ""Chapter 2. Almost commuting N-tuples""; ""2.1. An invariant for almost commuting N-tuples""; ""2.2. The case of rank zero""; ""2.3. The case of arbitrary rank"" 327 $a""Chapter 3. Some characterizations of groups of type A""""3.1. Generalities on subroot systems""; ""3.2. Action of CG on an alcove""; ""3.3. A first characterization of groups of type A""; ""3.4. Subgroups associated with elements of the center""; ""3.5. A further characterization of products of groups of type A""; ""3.6. A consequence of Proposition 3.5.1""; ""3.7. Application to generalized Cartan matrices and affine diagrams""; ""3.8. Numerology of clockwise symmetry""; ""Chapter 4. c-pairs""; ""4.1. The rank zero case""; ""4.2. The general case""; ""Chapter 5. Commuting triples"" 327 $a""5.1. Commuting triples of rank zero""""5.2. A list of all simple groups with rank zero commuting triples""; ""5.3. Action of the outer automorphism group of G""; ""5.4. Action of the center of G""; ""5.5. The general case""; ""Chapter 6. Some results on diagram automorphisms and associated root systems""; ""6.1. A chamber structure and a Coxeter group on the fixed subspace""; ""6.2. The restricted root system and the projection root system""; ""6.3. Generalized Cartan matrices for I??[sup(res)](l) and I??[sup(proj)](l)[sup(v)]""; ""6.4. The case of an outer automorphism"" 327 $a""6.5. Further results under an additional hypothesis""""6.6. The case of a subgroup of CI??""; ""6.7. Proof of Theorem 1.6.2""; ""Chapter 7. The fixed subgroup of an automorphism""; ""7.1. A first description of the component group""; ""7.2. Special automorphisms""; ""7.3. A complete description of the component group""; ""7.4. The roots of H[sup(I??)]""; ""7.5. The case of c-pairs""; ""7.6. Variation of I??[sub(0)](Z(x,y)) as x varies""; ""Chapter 8. C-triples""; ""8.1. c-triples of rank zero""; ""8.2. The maximal torus of a c-triple of order k""; ""8.3. The number of components"" 327 $a""10.2. Flat connections and the Chern-Simons invariant"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 747. 606 $aLie groups 606 $aCompact groups 606 $aRoot systems (Algebra) 615 0$aLie groups. 615 0$aCompact groups. 615 0$aRoot systems (Algebra) 676 $a510 s 676 $a512/.55 700 $aBorel$b Armand$045077 702 $aFriedman$b Robert$f1955- 702 $aMorgan$b John$f1946 March 21- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910812749903321 996 $aAlmost commuting elements in compact Lie groups$93952115 997 $aUNINA