Quantum groups and knot invariants:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Paris
Soc. Math. de France
1997
|
| Series: | Panoramas et synthèses
5 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 115 S. |
| ISBN: | 2856290558 |
Staff View
MARC
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| 245 | 1 | 0 | |a Quantum groups and knot invariants |c Christian Kassel ; Marc Rosso ; Vladimir Turaev |
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| 650 | 7 | |a Théorie des noeuds |2 rasuqam | |
| 650 | 4 | |a Categories (Mathematics) | |
| 650 | 4 | |a Knot theory | |
| 650 | 4 | |a Quantum groups | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
INTRODUCTION 1
1. THE YANG BAXTER EQUATION AND BRAID GROUP
REPRESENTATIONS 5
1.1. The Yang Baxter Equation 5
1.2. Artin s Braid Groups 7
1.3. Alternative description of Bn 8
2. HOPF ALGEBRAS AND MONOIDAL CATEGORIES 11
2.1. Hopf Algebras 11
2.2. Monoidal Categories 15
2.3. Braidings 18
2.4. Braided Bialgebras 19
3. DRINFELD S QUANTUM DOUBLE 23
3.1. The Dual Double Construction 23
3.2. The Quantum Double and its Properties 26
3.3. Hopf Pairings and a Generalized Double 30
4. THE QUANTIZED ENVELOPING ALGEBRA Uqsl(N + 1) 35
4.1. The Lie Algebra sl{N + 1) 35
4.2. Construction of Uq sl{N + 1) 36
4.3. A Poincare Birkhoff Witt Type Basis in U+ 39
4.4. Specializations and the Universal fl Matrix 42
vi CONTENTS
5. THE JONES POLYNOMIAL AND SKEIN CATEGORIES 45
5.1. Knots, Links, and Link Diagrams 45
5.2. The Jones Polynomial of Links 48
5.3. Skein Modules of Tangles 52
5.4. Categories of Tangles 55
6. FROM RIBBON CATEGORIES TO TOPOLOGICAL
INVARIANTS OF LINKS AND 3 MANIFOLDS 59
6.1. Ribbon Categories 59
6.2. The Functor F 62
6.3. Modular Categories 65
6.4. Invariants of 3 Manifolds 67
7. THE REPRESENTATION THEORY OF Uqsl(N + l) 71
7.1. Highest Weight Modules 71
7.2. Quantum Theory of Invariants 74
7.3. The Case of Roots of Unity 76
7.4. Quantum Groups with a Formal Parameter 79
8. VASSILIEV INVARIANTS OF LINKS 81
8.1. Definition and Examples 81
8.2. Chord Diagrams and Kontsevich s Theorem 84
8.3. The Pro Unipotent Completion of a Braided Category 85
8.4. Another description of %{R) 87
9. ADVANCED TOPICS 91
9.1. Infinitesimal Symmetric Categories 91
9.2. Quantization of an Infinitesimal Symmetric Category 95
9.3. The Kontsevich Universal Invariant 100
9.4. An Action of Gal(Q/Q) 102
GUIDE TO THE LITERATURE 105
INDEX 113
PANORAMAS ET SYNTHESES
|
| any_adam_object | 1 |
| author | Kassel, Christian Rosso, Marc Turaev, Vladimir G. 1954- |
| author_GND | (DE-588)122717791 |
| author_facet | Kassel, Christian Rosso, Marc Turaev, Vladimir G. 1954- |
| author_role | aut aut aut |
| author_sort | Kassel, Christian |
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| building | Verbundindex |
| bvnumber | BV012712840 |
| callnumber-first | Q - Science |
| callnumber-label | QC20 |
| callnumber-raw | QC20.7.G76 |
| callnumber-search | QC20.7.G76 |
| callnumber-sort | QC 220.7 G76 |
| callnumber-subject | QC - Physics |
| classification_rvk | SI 693 SK 300 |
| ctrlnum | (OCoLC)37857223 (DE-599)BVBBV012712840 |
| dewey-full | 512.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.55 |
| dewey-search | 512.55 |
| dewey-sort | 3512.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012712840 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:32:22Z |
| institution | BVB |
| isbn | 2856290558 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008641853 |
| oclc_num | 37857223 |
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| owner_facet | DE-384 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-83 |
| physical | VI, 115 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Soc. Math. de France |
| record_format | marc |
| series | Panoramas et synthèses |
| series2 | Panoramas et synthèses |
| spelling | Kassel, Christian Verfasser aut Quantum groups and knot invariants Christian Kassel ; Marc Rosso ; Vladimir Turaev Paris Soc. Math. de France 1997 VI, 115 S. txt rdacontent n rdamedia nc rdacarrier Panoramas et synthèses 5 Groupe quantique rasuqam Invariant rasuqam Théorie des catégories rasuqam Théorie des noeuds rasuqam Categories (Mathematics) Knot theory Quantum groups Three-manifolds (Topology) Quantengruppe (DE-588)4252437-4 gnd rswk-swf Invariante (DE-588)4128781-2 gnd rswk-swf Knoten Mathematik (DE-588)4164314-8 gnd rswk-swf Quantengruppe (DE-588)4252437-4 s Knoten Mathematik (DE-588)4164314-8 s Invariante (DE-588)4128781-2 s DE-604 Rosso, Marc Verfasser aut Turaev, Vladimir G. 1954- Verfasser (DE-588)122717791 aut Panoramas et synthèses 5 (DE-604)BV037491878 5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008641853&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kassel, Christian Rosso, Marc Turaev, Vladimir G. 1954- Quantum groups and knot invariants Panoramas et synthèses Groupe quantique rasuqam Invariant rasuqam Théorie des catégories rasuqam Théorie des noeuds rasuqam Categories (Mathematics) Knot theory Quantum groups Three-manifolds (Topology) Quantengruppe (DE-588)4252437-4 gnd Invariante (DE-588)4128781-2 gnd Knoten Mathematik (DE-588)4164314-8 gnd |
| subject_GND | (DE-588)4252437-4 (DE-588)4128781-2 (DE-588)4164314-8 |
| title | Quantum groups and knot invariants |
| title_auth | Quantum groups and knot invariants |
| title_exact_search | Quantum groups and knot invariants |
| title_full | Quantum groups and knot invariants Christian Kassel ; Marc Rosso ; Vladimir Turaev |
| title_fullStr | Quantum groups and knot invariants Christian Kassel ; Marc Rosso ; Vladimir Turaev |
| title_full_unstemmed | Quantum groups and knot invariants Christian Kassel ; Marc Rosso ; Vladimir Turaev |
| title_short | Quantum groups and knot invariants |
| title_sort | quantum groups and knot invariants |
| topic | Groupe quantique rasuqam Invariant rasuqam Théorie des catégories rasuqam Théorie des noeuds rasuqam Categories (Mathematics) Knot theory Quantum groups Three-manifolds (Topology) Quantengruppe (DE-588)4252437-4 gnd Invariante (DE-588)4128781-2 gnd Knoten Mathematik (DE-588)4164314-8 gnd |
| topic_facet | Groupe quantique Invariant Théorie des catégories Théorie des noeuds Categories (Mathematics) Knot theory Quantum groups Three-manifolds (Topology) Quantengruppe Invariante Knoten Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008641853&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV037491878 |
| work_keys_str_mv | AT kasselchristian quantumgroupsandknotinvariants AT rossomarc quantumgroupsandknotinvariants AT turaevvladimirg quantumgroupsandknotinvariants |