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Almost commuting elements in compact Lie groups / / Armand Borel, Robert Friedman, John W. Morgan
| Almost commuting elements in compact Lie groups / / Armand Borel, Robert Friedman, John W. Morgan |
| Autore | Borel Armand |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2002] |
| Descrizione fisica | 1 online resource (153 p.) |
| Disciplina |
510 s
512/.55 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Lie groups
Compact groups Root systems (Algebra) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0340-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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(Ï?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""
""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"" ""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 Î?[sup(res)](l) and Î?[sup(proj)](l)[sup(v)]""; ""6.4. The case of an outer automorphism"" ""6.5. Further results under an additional hypothesis""""6.6. The case of a subgroup of CÎ?""; ""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(Ï?)]""; ""7.5. The case of c-pairs""; ""7.6. Variation of Ï€[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"" ""10.2. Flat connections and the Chern-Simons invariant"" |
| Record Nr. | UNINA-9910480939903321 |
Borel Armand
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2002] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Almost commuting elements in compact Lie groups / / Armand Borel, Robert Friedman, John W. Morgan
| Almost commuting elements in compact Lie groups / / Armand Borel, Robert Friedman, John W. Morgan |
| Autore | Borel Armand |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2002] |
| Descrizione fisica | 1 online resource (153 p.) |
| Disciplina |
510 s
512/.55 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Lie groups
Compact groups Root systems (Algebra) |
| ISBN | 1-4704-0340-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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(Ï?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""
""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"" ""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 Î?[sup(res)](l) and Î?[sup(proj)](l)[sup(v)]""; ""6.4. The case of an outer automorphism"" ""6.5. Further results under an additional hypothesis""""6.6. The case of a subgroup of CÎ?""; ""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(Ï?)]""; ""7.5. The case of c-pairs""; ""7.6. Variation of Ï€[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"" ""10.2. Flat connections and the Chern-Simons invariant"" |
| Record Nr. | UNINA-9910788846203321 |
|
Borel Armand
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2002] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Almost commuting elements in compact Lie groups / / Armand Borel, Robert Friedman, John W. Morgan
| Almost commuting elements in compact Lie groups / / Armand Borel, Robert Friedman, John W. Morgan |
| Autore | Borel Armand |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2002] |
| Descrizione fisica | 1 online resource (153 p.) |
| Disciplina |
510 s
512/.55 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Lie groups
Compact groups Root systems (Algebra) |
| ISBN | 1-4704-0340-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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(Ï?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""
""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"" ""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 Î?[sup(res)](l) and Î?[sup(proj)](l)[sup(v)]""; ""6.4. The case of an outer automorphism"" ""6.5. Further results under an additional hypothesis""""6.6. The case of a subgroup of CÎ?""; ""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(Ï?)]""; ""7.5. The case of c-pairs""; ""7.6. Variation of Ï€[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"" ""10.2. Flat connections and the Chern-Simons invariant"" |
| Record Nr. | UNINA-9910812749903321 |
|
Borel Armand
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2002] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||