Fusion of defects:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2019]
|
| Series: | Memoirs of the American Mathematical Society
volume 258, number 1237 first of 7 numbers) |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | vii, 100 Seiten |
| ISBN: | 9781470435233 |
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MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Acknowledgments vii
Introduction 1
A. Conformal nets 1
B. Defects 2
c. Sectors 2
D. The vacuum sector of a defect 3
E. Composition of defects 3
F. Fusion of sectors and the interchange isomorphism 4
G. The 1 13 1-isomorphism 5
H. Construction of the 1 13 1-isomorphism 5
Chapter 1. Defects 9
l.A. Bicolored intervals and circles 9
l.B. Definition of defects 10
l.C. Examples of defects 16
l.D. The category CNi of defects 22
l.E. Composition of defects 23
1. F. Associativity of composition 26
Chapter 2. Sectors 29
2. A. The category CN2 of sectors 29
2.B. Horizontal fusion 31
2. C. Vertical fusion 32
Chapter 3. Properties of the composition of defects 35
3. A. Left and right units 35
3. B. Semisimplicity of the composite defect 37
Chapter 4. A variant of horizontal fusion 43
4. A. The keyhole and keystone fusion 43
4.B. The keyhole fusion of vacuum sectors of defects 46
4.C. The keystone fusion of vacuum sectors of defects 49
4. D. Comparison between fusion and keystone fusion 53
Chapter 5. Haag duality for composition of defects 57
5. A. The dimension of the Haag inclusion 60
5.B. The double bridge algebra is a factor 61
5.C. The dimension of the bridge inclusions 62
in
IV
CONTENTS
Chapter 6. The 13 1-isomorphism 65
6.A. The 113 1-inap is an isomorphism 65
6.B. The 1 3 1-isomorphism for an identity defect 67
6.C. Unitors for horizontal fusion of sectors 72
6.D. The interchange isomorphism 75
Appendix A. Components for the 3-category of conformal nets 77
Appendix B. Von Neumann algebras 79
B.L The Haagerup X2-space 79
B.II. Connes fusion 80
B.III. Cyclic fusion 80
B.IV. Fusion and fiber product of von Neumann algebras 81
B.V. Compatibility with tensor products 81
B.VL Dualizability 82
B.VII. Statistical dimension and minimal index 82
B.VIII. Functors between module categories 83
B.IX. The split property 84
B. X. Two-sided fusion on L2-spaces 86
Appendix C. Conformal nets 91
C. I. Axioms for conformal nets 91
C.IL The vacuum sector 92
C.IIL Gluing vacuum sectors 93
C.IV. Finite-index conformal nets 94
C.V. Sectors and the Hilbert space of the annulus 94
C.VI. Extension of conformal nets to all 1-manifolds 95
Appendix D. Diagram of dependencies 97
Bibliography 99
|
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| author | Bartels, Arthur Douglas, Christopher L. Henriques, André |
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| id | DE-604.BV045877305 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:29:10Z |
| institution | BVB |
| isbn | 9781470435233 |
| language | English |
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| physical | vii, 100 Seiten |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Bartels, Arthur aut Fusion of defects Arthur Bartels, Christopher L. Douglas, André Henriques Providence, Rhode Island American Mathematical Society [2019] © 2019 vii, 100 Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 258, number 1237 first of 7 numbers) Douglas, Christopher L. (DE-588)1066804842 aut Henriques, André aut Memoirs of the American Mathematical Society volume 258, number 1237 first of 7 numbers) (DE-604)BV008000141 1237 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031260503&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bartels, Arthur Douglas, Christopher L. Henriques, André Fusion of defects Memoirs of the American Mathematical Society |
| title | Fusion of defects |
| title_auth | Fusion of defects |
| title_exact_search | Fusion of defects |
| title_full | Fusion of defects Arthur Bartels, Christopher L. Douglas, André Henriques |
| title_fullStr | Fusion of defects Arthur Bartels, Christopher L. Douglas, André Henriques |
| title_full_unstemmed | Fusion of defects Arthur Bartels, Christopher L. Douglas, André Henriques |
| title_short | Fusion of defects |
| title_sort | fusion of defects |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031260503&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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