Kac algebras arising from composition of subfactors: general theory and classification
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
2002
|
| Series: | Memoirs of the American Mathematical Society
750 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 158, number 750 (first of 4 numbers)." |
| Physical Description: | IX, 198 S. |
| ISBN: | 0821829351 |
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| 100 | 1 | |a Izumi, Masaki |d 1965- |e Verfasser |0 (DE-588)1146371373 |4 aut | |
| 245 | 1 | 0 | |a Kac algebras arising from composition of subfactors |b general theory and classification |c Masaki Izumi ; Hideki Ksaki |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2002 | |
| 300 | |a IX, 198 S. | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v 750 | |
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Record in the Search Index
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| adam_text | Contents
ix
Chapter 1. Introduction 1
Chapter 2. Actions of matched pairs 5
1. Cocycles and cohomology group 6
2. Cocycle conjugacy 11
3. Appendix Iterated perturbation 17
4. Appendix Normalization of cocycles 18
Chapter 3. Cocycles attached to the pentagon equation 21
1. Cocycles 21
2. Cohomology group 25
3. Appendix Normalization of cocycles 27
4. Appendix Multiplicative unitary Ve 28
Chapter 4. Multiplicative unitary 31
1. Preliminaries 31
2. Orthonormal basis and multiplicative unitary 33
Chapter 5. Kac algebra structure 37
Chapter 6. Group like elements 43
Chapter 7. Examples of finite dimensional Kac algebras 49
1. (Zn x Zn) x Z2 with n 3 49
2. (Z2 x Z2) x. Z2 50
3. (Zn x Zn) x. Z2 with n 2 52
4. (Zn x Zn) x Z2 with n even 53
5. D2n x Z2 with n odd 56
6. .D2n x Z2 with n even 58
Chapter 8. Inclusions with the Coxeter Dynkin graph D6 and the Kac
Paljutkin algebra 63
1. The group of one dimensional sectors 63
2. Kac Paljutkin algebra 66
Chapter 9. Structure theorems 71
1. Preliminaries 72
2. Main theorem 73
3. Proof 76
vii
viii CONTENTS
Chapter 10. Classification of certain Kac algebras 83
1. Useful criteria 83
2. 3p theorem 86
3. p2q case 88
4. Classification of low dimensional Kac algebras 96
Chapter 11. Classification of Kac algebras of dimension 16 107
1. Case when G(A) is an abelian group of order 8 107
2. Computation of the invariant H2({D8, Z2), T)/~ 112
3. Classification 116
Chapter 12. Group extensions of general Kac algebras 123
1. Description of cocycles 123
2. Multiplicative unitary 130
Chapter 13. 2 cocycles of Kac algebras 141
1. Preliminaries 141
2. Ergodic actions and 2 cocycles 145
3. Examples I Kac Paljutkin algebra 147
4. Examples II Group algebras 154
Chapter 14. Classification of Kac algebras of dimension 24 159
1. Preliminaries 159
2. Computation of H2((TV, H), T)/~ 164
3. Reduction to the semi direct product case 178
4. Classification 187
Bibliography 193
Index 196
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 512 - Algebra |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV014410863 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:02:27Z |
| institution | BVB |
| isbn | 0821829351 |
| language | English |
| lccn | 2002018393 |
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| physical | IX, 198 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Izumi, Masaki 1965- Verfasser (DE-588)1146371373 aut Kac algebras arising from composition of subfactors general theory and classification Masaki Izumi ; Hideki Ksaki Providence, R.I. American Mathematical Society 2002 IX, 198 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 750 "Volume 158, number 750 (first of 4 numbers)." C*-algebra's gtt Kac-Moody algebras Kac-Moody-Algebra (DE-588)4223399-9 gnd rswk-swf Kac-Moody-Algebra (DE-588)4223399-9 s DE-604 Kosaki, Hideki 1950- Sonstige (DE-588)1033199427 oth Memoirs of the American Mathematical Society 750 (DE-604)BV008000141 750 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009856301&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Izumi, Masaki 1965- Kac algebras arising from composition of subfactors general theory and classification Memoirs of the American Mathematical Society C*-algebra's gtt Kac-Moody algebras Kac-Moody-Algebra (DE-588)4223399-9 gnd |
| subject_GND | (DE-588)4223399-9 |
| title | Kac algebras arising from composition of subfactors general theory and classification |
| title_auth | Kac algebras arising from composition of subfactors general theory and classification |
| title_exact_search | Kac algebras arising from composition of subfactors general theory and classification |
| title_full | Kac algebras arising from composition of subfactors general theory and classification Masaki Izumi ; Hideki Ksaki |
| title_fullStr | Kac algebras arising from composition of subfactors general theory and classification Masaki Izumi ; Hideki Ksaki |
| title_full_unstemmed | Kac algebras arising from composition of subfactors general theory and classification Masaki Izumi ; Hideki Ksaki |
| title_short | Kac algebras arising from composition of subfactors |
| title_sort | kac algebras arising from composition of subfactors general theory and classification |
| title_sub | general theory and classification |
| topic | C*-algebra's gtt Kac-Moody algebras Kac-Moody-Algebra (DE-588)4223399-9 gnd |
| topic_facet | C*-algebra's Kac-Moody algebras Kac-Moody-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009856301&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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