Squared Hopf algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Soc.
1999
|
| Schriftenreihe: | American Mathematical Society: Memoirs of the American Mathematical Society
677 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 180 S. graph. Darst. |
| ISBN: | 0821813617 |
Internformat
MARC
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| 245 | 1 | 0 | |a Squared Hopf algebras |c Volodymyr V. Lyubashenko |
| 264 | 1 | |a Providence, RI |b American Mathematical Soc. |c 1999 | |
| 300 | |a IX, 180 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1804127588758585344 |
|---|---|
| adam_text | Contents
Introduction 1
Chapter 1. Tools 5
1.1. Tensor product of abelian categories 5
1.2. Monoidal categories 7
1.3. Monoidal abelian categories 23
1.4. Symmetric monoidal 2 category of abelian categories 24
1.5. System of notations 24
1.6. Monoidal structures on V El V 32
1.7. Ind objects 34
1.8. Rigid abelian categories 37
Chapter 2. Squared coalgebras 43
2.1. Definitions 43
2.2. Comodules 47
2.3. The fundamental theorem on coalgebras 48
2.4. Relationship between categories of comodules 50
2.5. The category of fibre functors 51
2.6. Reconstruction theorems 55
2.7. Comodules over ordinary coalgebras 60
2.8. Construction data 61
Chapter 3. Squared bicoalgebras 65
3.1. Tensor product of squared coalgebras 65
3.2. Bicoalgebras 68
3.3. Monoidal construction data 69
3.4. Tensor generators and relations 77
3.5. Relationship with braided bialgebras 82
3.6. Commutative algebras and braiding 85
Chapter 4. Hopf coalgebras 87
4.1. Opposite coalgebras 87
4.2. Comparison with opposite coalgebra in braided case 91
4.3. The antipode 92
4.4. Comparison with braided Hopf algebras 103
4.5. Multiplication in the opposite bialgebra 105
4.6. Reconstruction of rigid monoidal categories 116
Chapter 5. Quasitriangular Hopf coalgebras 121
5.1. /^ matrices in Hopf coalgebras 121
vii
viii CONTENTS
5.2. Braiding for comodules over a braided Hopf algebra 126
5.3. Constructing braided categories 127
5.4. Ribbon Hopf coalgebras 129
5.5. Ribbon reconstruction 131
Appendix A. Symmetric monoidal 2 categories 134
A.I. A review of 2 categories 134
A.2. 2 pasting schemes 136
A.3. Weak 2 pasting 141
A.4. Weak 3 categories 148
A.5. A monoidal 2 category of abelian categories 150
A.6. Symmetric monoidal 2 categories 173
A.7. A symmetric monoidal 2 category of abelian categories 175
Bibliography 179
|
| any_adam_object | 1 |
| author | Ljubašenko, Volodymyr V. 1959- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:35:44Z |
| institution | BVB |
| isbn | 0821813617 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008782096 |
| oclc_num | 247592694 |
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| physical | IX, 180 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | American Mathematical Soc. |
| record_format | marc |
| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spelling | Ljubašenko, Volodymyr V. 1959- Verfasser (DE-588)173349269 aut Squared Hopf algebras Volodymyr V. Lyubashenko Providence, RI American Mathematical Soc. 1999 IX, 180 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Memoirs of the American Mathematical Society 677 Hopf-Algebra (DE-588)4160646-2 gnd rswk-swf Hopf-Algebra (DE-588)4160646-2 s DE-604 American Mathematical Society: Memoirs of the American Mathematical Society 677 (DE-604)BV008000141 677 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008782096&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ljubašenko, Volodymyr V. 1959- Squared Hopf algebras American Mathematical Society: Memoirs of the American Mathematical Society Hopf-Algebra (DE-588)4160646-2 gnd |
| subject_GND | (DE-588)4160646-2 |
| title | Squared Hopf algebras |
| title_auth | Squared Hopf algebras |
| title_exact_search | Squared Hopf algebras |
| title_full | Squared Hopf algebras Volodymyr V. Lyubashenko |
| title_fullStr | Squared Hopf algebras Volodymyr V. Lyubashenko |
| title_full_unstemmed | Squared Hopf algebras Volodymyr V. Lyubashenko |
| title_short | Squared Hopf algebras |
| title_sort | squared hopf algebras |
| topic | Hopf-Algebra (DE-588)4160646-2 gnd |
| topic_facet | Hopf-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008782096&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT ljubasenkovolodymyrv squaredhopfalgebras |