Lectures on tensor categories and modular functors:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2001]
|
| Schriftenreihe: | University lecture series
Volume 21 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | x, 221 Seiten Diagramme |
| ISBN: | 0821826867 9780821826867 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804128472085299200 |
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| adam_text | UNIVERSITY LECTURE SERIES VOLUME 21 LECTURES ON TENSOR CATEGORIES AND
MODULAR FUNCTORS BOJKO BAKALOV ALEXANDER KIRILLOV, JR. AMERICAN
MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND CONTENTS INTRODUCTION
CHAPTER 1. BRAIDED TENSOR CATEGORIES 9 1.1. MONOIDAL TENSOR CATEGORIES 9
1.2. BRAIDED TENSOR CATEGORIES 15 1.3. QUANTUM GROUPS 19 1.4. DRINFELD S
CATEGORY 21 CHAPTER 2. RIBBON CATEGORIES 29 2.1. RIGID MONOIDAL
CATEGORIES 29 2.2. RIBBON CATEGORIES 33 2.3. GRAPHICAL CALCULUS FOR
MORPHISMS 35 2.4. SEMISIMPLE CATEGORIES 44 CHAPTER 3. MODULAR TENSOR
CATEGORIES 47 3.1. MODULAR TENSOR CATEGORIES 47 3.2. EXAMPLE: QUANTUM
DOUBLE OF A FINITE GROUP 59 3.3. QUANTUM GROUPS AT ROOTS OF UNITY 62
CHAPTER 4. 3-DIMENSIONAL TOPOLOGICAL QUANTUM FIELD THEORY 71 4.1.
INVARIANTS OF 3-MANIFOLDS 71 4.2. TOPOLOGICAL QUANTUM FIELD THEORY 76
4.3. 1+1 DIMENSIONAL TQFT 78 4.4. 3D TQFT FROM MTC 82 4.5. EXAMPLES 87
CHAPTER 5. MODULAR FUNCTORS 93 5.1. MODULAR FUNCTORS 93 5.2. THE LEGO
GAME 99 5.3. RIBBON CATEGORIES VIA THE HORN SPACES 108 5.4. MODULAR
FUNCTORS IN GENUS ZERO AND TENSOR CATEGORIES 116 5.5. MODULAR CATEGORIES
AND MODULAR FUNCTORS FOR ZERO CENTRAL CHARGE 119 5.6. TOWERS OF
GROUPOIDS 124 5.7. CENTRAL EXTENSIONS OF MODULAR FUNCTORS 130 5.8. FROM
2D MF TO 3D TQFT . 135 CHAPTER 6. MODULI SPACES AND COMPLEX MODULAR
FUNCTORS 141 6.1. MODULI SPACES AND COMPLEX TEICHMIILLER TOWER 141 6.2.
COMPACTIFICATION OF THE MODULI SPACE AND GLUING 147 6.3. CONNECTIONS
WITH REGULAR SINGULARITIES 152 6.4. COMPLEX-ANALYTIC MODULAR FUNCTORS
158 X CONTENTS 6.5. EXAMPLE: DRINFELD S CATEGORY 161 6.6. TWISTED
-MODULES 164 6.7. COMPLEX MODULAR FUNCTORS WITH CENTRAL CHARGE 167
CHAPTER 7. WESS-ZUMINO-WITTEN MODEL 173 7.1. PRELIMINARIES ON AFHNE LIE
ALGEBRAS 174 7.2. REMINDERS FROM ALGEBRAIC GEOMETRY 175 7.3. CONFORMAL
BLOCKS: DEFINITION 177 7.4. FLAT CONNECTION IN THE BUNDLE OF CONFORMAL
BLOCKS 181 7.5. FROM LOCAL PARAMETERS TO TANGENT VECTORS 188 7.6.
FAMILIES OF CURVES OVER A FORMAL BASE 191 7.7. COINVARIANTS FOR SINGULAR
CURVES 194 7.8. THE GLUING AXIOM FOR THE BUNDLE OF COINVARIANTS 195 7.9.
WZW MODULAR FUNCTOR 202 7.10. CALCULATION OF THE CENTRAL CHARGE 203
BIBLIOGRAPHY 213 INDEX 217 INDEX OF NOTATION 219
|
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| author | Bakalov, Bojko 1973- Kirillov, Alexander Jr. 1967- |
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| dewey-full | 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
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| dewey-tens | 510 - Mathematics |
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| id | DE-604.BV013659997 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:49:47Z |
| institution | BVB |
| isbn | 0821826867 9780821826867 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009334017 |
| oclc_num | 247746124 |
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| physical | x, 221 Seiten Diagramme |
| publishDate | 2001 |
| publishDateSearch | 2001 |
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| publisher | American Mathematical Society |
| record_format | marc |
| series | University lecture series |
| series2 | University lecture series |
| spelling | Bakalov, Bojko 1973- Verfasser (DE-588)1146317328 aut Lectures on tensor categories and modular functors Bojko Bakalov ; Alexander Kirillov, Jr. Providence, Rhode Island American Mathematical Society [2001] © 2001 x, 221 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier University lecture series Volume 21 Monoidale Kategorie - Topologische Quantenfeldtheorie Abelsche Kategorie (DE-588)4140991-7 gnd rswk-swf Tensorprodukt (DE-588)4059478-6 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Abelsche Kategorie (DE-588)4140991-7 s Tensorprodukt (DE-588)4059478-6 s Quantenfeldtheorie (DE-588)4047984-5 s DE-604 Kirillov, Alexander Jr. 1967- Verfasser (DE-588)135930243 aut Erscheint auch als Online-Ausgabe 978-1-4704-2168-7 University lecture series Volume 21 (DE-604)BV004153846 21 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009334017&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bakalov, Bojko 1973- Kirillov, Alexander Jr. 1967- Lectures on tensor categories and modular functors University lecture series Monoidale Kategorie - Topologische Quantenfeldtheorie Abelsche Kategorie (DE-588)4140991-7 gnd Tensorprodukt (DE-588)4059478-6 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4140991-7 (DE-588)4059478-6 (DE-588)4047984-5 |
| title | Lectures on tensor categories and modular functors |
| title_auth | Lectures on tensor categories and modular functors |
| title_exact_search | Lectures on tensor categories and modular functors |
| title_full | Lectures on tensor categories and modular functors Bojko Bakalov ; Alexander Kirillov, Jr. |
| title_fullStr | Lectures on tensor categories and modular functors Bojko Bakalov ; Alexander Kirillov, Jr. |
| title_full_unstemmed | Lectures on tensor categories and modular functors Bojko Bakalov ; Alexander Kirillov, Jr. |
| title_short | Lectures on tensor categories and modular functors |
| title_sort | lectures on tensor categories and modular functors |
| topic | Monoidale Kategorie - Topologische Quantenfeldtheorie Abelsche Kategorie (DE-588)4140991-7 gnd Tensorprodukt (DE-588)4059478-6 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| topic_facet | Monoidale Kategorie - Topologische Quantenfeldtheorie Abelsche Kategorie Tensorprodukt Quantenfeldtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009334017&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004153846 |
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