Almost commuting elements in compact Lie groups:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
AMS
2002
|
| Series: | Memoirs of the American Mathematical Society
747 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 157, number 747 (third of 5 numbers)." |
| Physical Description: | X, 136 S. |
| ISBN: | 0821827928 |
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MARC
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| 245 | 1 | 0 | |a Almost commuting elements in compact Lie groups |c Armand Borel ; Robert Friedman ; John W. Morgan |
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v 747 | |
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Record in the Search Index
| _version_ | 1804129223140442113 |
|---|---|
| adam_text | Contents
Chapter 1. Introduction 1
1.1. Preliminaries 2
1.2. The case of commuting pairs in a simply connected group 4
1.3. c pairs 4
1.4. Commuting triples 5
1.5. C triples 6
1.6. Quotients of diagram automorphisms 7
1.7. Description of 5(Ar) and SWc(g,k) 8
1.8. Chern Simons invariants and Witten s Clockwise Symmetry
Conjecture 9
1.9. Outline of the paper 11
1.10. History 13
Chapter 2. Almost commuting JV tuples 15
2.1. An invariant for almost commuting JV tuples 15
2.2. The case of rank zero 16
2.3. The case of arbitrary rank 18
Chapter 3. Some characterizations of groups of type A 21
3.1. Generalities on subroot systems 21
3.2. Action of CG on an alcove 21
3.3. A first characterization of groups of type A 24
3.4. Subgroups associated with elements of the center 25
3.5. A further characterization of products of groups of type A 26
3.6. A consequence of Proposition 3.5.1 27
3.7. Application to generalized Cartan matrices and affine diagrams 28
3.8. Numerology of clockwise symmetry 30
Chapter 4. c pairs 35
4.1. The rank zero case 35
4.2. The general case 37
Chapter 5. Commuting triples 39
5.1. Commuting triples of rank zero 39
5.2. A list of all simple groups with rank zero commuting triples 41
5.3. Action of the outer automorphism group of G 41
5.4. Action of the center of G 41
5.5. The general case 42
vii
viii CONTENTS
Chapter 6. Some results on diagram automorphisms and associated root
systems 47
6.1. A chamber structure and a Coxeter group on the fixed subspace 47
6.2. The restricted root system and the projection root system 49
6.3. Generalized Cartan matrices for (f) and °J(^)v 53
6.4. The case of an outer automorphism 56
6.5. Further results under an additional hypothesis 58
6.6. The case of a subgroup of C 3 59
6.7. Proof of Theorem 1.6.2 61
Chapter 7. The fixed subgroup of an automorphism 63
7.1. A first description of the component group 63
7.2. Special automorphisms 65
7.3. A complete description of the component group 67
7.4. The roots of Ha 72
7.5. The case of c pairs 73
7.6. Variation of tto(Z(x, y)) as x varies 75
Chapter 8. C triples 77
8.1. c triples of rank zero 77
8.2. The maximal torus of a c triple of order k 83
8.3. The number of components 87
8.4. Proof of Parts 1,2,3 of Theorem 1.5.1 for (C) cyclic 88
8.5. Proof of Part 4 of Theorem 1.5.1 for (C) cyclic 89
Chapter 9. The tori S{k) and ~SWC (g, k) and their Weyl groups 91
9.1. A root system on f(k) 91
9.2. Completion of the proof of Theorem 1.4.1 95
9.3. Completion of the proof of Theorem 1.5.1 in case (C) is cyclic 95
9.4. The generalized Cartan matrix associated to Av — /v(n, fc) C t(n, k) 96
9.5. Proof of Theorem 1.7.4 99
Chapter 10. The Chern Simons invariant 101
10.1. An algebraic invariant of c triples 101
10.2. Flat connections and the Chern Simons invariant 108
10.3. The basic computation 113
10.4. Proof of Theorem 1.8.1 and Theorem 1.8.2 in the case where (C) is
cyclic 116
Chapter 11. The case when (C) is not cyclic 119
11.1. Rank zero C triples 119
11.2. Action of the center and of the outer automorphism group 121
11.3. The general case 121
11.4. Chern Simons invariants 124
11.5. Proof of Theorem 1.8.1 and Theorem 1.8.2 when (C) is not cyclic 126
Bibliography 127
Diagrams and tables 129
Extended coroot diagrams and extended coroot integers 129
CONTENTS ix
Quotient extended coroot diagrams and quotient coroot integers 132
Root systems on twc 135
Root systems on t(k) for fc 1 136
Root systems on twc (g, k) for (C) ^ 1 and k n0 136
|
| any_adam_object | 1 |
| author | Borel, Armand 1923-2003 Friedman, Robert 1950- Morgan, John W. 1946- |
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| discipline | Mathematik |
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| indexdate | 2024-07-09T19:01:43Z |
| institution | BVB |
| isbn | 0821827928 |
| language | English |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Borel, Armand 1923-2003 Verfasser (DE-588)119089106 aut Almost commuting elements in compact Lie groups Armand Borel ; Robert Friedman ; John W. Morgan Providence, RI AMS 2002 X, 136 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 747 "Volume 157, number 747 (third of 5 numbers)." Lie-algebra's gtt Lie-groepen gtt Compact groups Lie groups Root systems (Algebra) Kompakte Gruppe (DE-588)4164840-7 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 s Kompakte Gruppe (DE-588)4164840-7 s DE-604 Friedman, Robert 1950- Verfasser (DE-588)174092032 aut Morgan, John W. 1946- Verfasser (DE-588)129352446 aut Memoirs of the American Mathematical Society 747 (DE-604)BV008000141 747 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009827221&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Borel, Armand 1923-2003 Friedman, Robert 1950- Morgan, John W. 1946- Almost commuting elements in compact Lie groups Memoirs of the American Mathematical Society Lie-algebra's gtt Lie-groepen gtt Compact groups Lie groups Root systems (Algebra) Kompakte Gruppe (DE-588)4164840-7 gnd Lie-Gruppe (DE-588)4035695-4 gnd |
| subject_GND | (DE-588)4164840-7 (DE-588)4035695-4 |
| title | Almost commuting elements in compact Lie groups |
| title_auth | Almost commuting elements in compact Lie groups |
| title_exact_search | Almost commuting elements in compact Lie groups |
| title_full | Almost commuting elements in compact Lie groups Armand Borel ; Robert Friedman ; John W. Morgan |
| title_fullStr | Almost commuting elements in compact Lie groups Armand Borel ; Robert Friedman ; John W. Morgan |
| title_full_unstemmed | Almost commuting elements in compact Lie groups Armand Borel ; Robert Friedman ; John W. Morgan |
| title_short | Almost commuting elements in compact Lie groups |
| title_sort | almost commuting elements in compact lie groups |
| topic | Lie-algebra's gtt Lie-groepen gtt Compact groups Lie groups Root systems (Algebra) Kompakte Gruppe (DE-588)4164840-7 gnd Lie-Gruppe (DE-588)4035695-4 gnd |
| topic_facet | Lie-algebra's Lie-groepen Compact groups Lie groups Root systems (Algebra) Kompakte Gruppe Lie-Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009827221&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT borelarmand almostcommutingelementsincompactliegroups AT friedmanrobert almostcommutingelementsincompactliegroups AT morganjohnw almostcommutingelementsincompactliegroups |