Frobenius and separable functors for generalized module categories and nonlinear equations:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London
Springer
2002
|
| Series: | Lecture notes in mathematics
1787 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 354 S. |
| ISBN: | 3540437827 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Table of Contents
Part I Entwined modules and Doi Koppinen Hopf modules
1 Generalities 3
1.1 Coalgebras, bialgebras, and Hopf algebras 3
1.2 Adjoint functors 22
1.3 Separable algebras and Frobenius algebras 28
2 Doi Koppinen Hopf modules and entwined modules 39
2.1 Doi Koppinen structures and entwining structures 39
2.2 Doi Koppinen modules and entwined modules 48
2.3 Entwined modules and the smash product 50
2.4 Entwined modules and the smash coproduct 59
2.5 Adjoint functors for entwined modules 64
2.6 Two sided entwined modules 68
2.7 Entwined modules and comodules over a coring 71
2.8 Monoidal categories 78
3 Frobenius and separable functors for entwined modules ... 89
3.1 Separable functors and Frobenius functors 89
3.2 Restriction of scalars and the smash product 99
3.3 The functor forgetting the C coaction 124
3.4 The functor forgetting the ^ action 137
3.5 The general induction functor 146
4 Applications 159
4.1 Relative Hopf modules 159
4.2 Hopf Galois extensions 168
4.3 Doi s [H, q modules 179
4.4 Yetter Drinfeld modules 181
4.5 Long dimodules 193
4.6 Modules graded by G sets 195
4.7 Two sided entwined modules revisited 198
4.8 Corings and descent theory 204
XIV Table of Contents
Part II Nonlinear equations
5 Yetter Drinfeld modules and the quantum Yang Baxter
equation 217
5.1 Notation 217
5.2 The quantum Yang Baxter equation and the braid equation. . 218
5.3 Hopf algebras versus the QYBE 225
5.4 The FRT Theorem 235
5.5 The set theoretic braid equation 238
6 Hopf modules and the pentagon equation 245
6.1 The Hopf equation and the pentagon equation 245
6.2 The FRT Theorem for the Hopf equation 253
6.3 New examples of noncommutative noncocommutative
bialgebras 267
6.4 The pentagon equation versus the structure and the
classification of finite dimensional Hopf algebras 277
7 Long dimodules and the Long equation 301
7.1 The Long equation 301
7.2 The FRT Theorem for the Long equation 304
7.3 Long coalgebras 311
8 The Frobenius Separability equation 317
8.1 Frobenius algebras and separable algebras 317
8.2 The Frobenius separability equation 320
8.3 The structure of Frobenius algebras and separable algebras . . 332
8.4 The category of FS objects 339
References 345
Index 353
|
| any_adam_object | 1 |
| author | Caenepeel, Stefaan 1956- Militaru, Gigel 1966- Zhu, Shenglin 1964- |
| author_GND | (DE-588)123804132 (DE-588)123804183 (DE-588)123804213 |
| author_facet | Caenepeel, Stefaan 1956- Militaru, Gigel 1966- Zhu, Shenglin 1964- |
| author_role | aut aut aut |
| author_sort | Caenepeel, Stefaan 1956- |
| author_variant | s c sc g m gm s z sz |
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| dewey-ones | 510 - Mathematics |
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| indexdate | 2024-07-09T19:01:38Z |
| institution | BVB |
| isbn | 3540437827 |
| language | English |
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| physical | XIV, 354 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Caenepeel, Stefaan 1956- Verfasser (DE-588)123804132 aut Frobenius and separable functors for generalized module categories and nonlinear equations Stefaan Caenepeel ; Gigel Militaru ; Shenglin Zhu Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London Springer 2002 XIV, 354 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1787 Separable Algebra - Frobenius-Algebra - Modulkategorie - Funktor - Nichtlineare Gleichung Differential equations, Nonlinear Frobenius algebras Modules (Algebra) Nichtlineare Gleichung (DE-588)4455337-7 gnd rswk-swf Funktor (DE-588)4130706-9 gnd rswk-swf Modulkategorie (DE-588)4170335-2 gnd rswk-swf Frobenius-Algebra (DE-588)4155476-0 gnd rswk-swf Separable Algebra (DE-588)4181009-0 gnd rswk-swf Separable Algebra (DE-588)4181009-0 s Frobenius-Algebra (DE-588)4155476-0 s Modulkategorie (DE-588)4170335-2 s Funktor (DE-588)4130706-9 s Nichtlineare Gleichung (DE-588)4455337-7 s DE-604 Militaru, Gigel 1966- Verfasser (DE-588)123804183 aut Zhu, Shenglin 1964- Verfasser (DE-588)123804213 aut Lecture notes in mathematics 1787 (DE-604)BV000676446 1787 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009823770&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Caenepeel, Stefaan 1956- Militaru, Gigel 1966- Zhu, Shenglin 1964- Frobenius and separable functors for generalized module categories and nonlinear equations Lecture notes in mathematics Separable Algebra - Frobenius-Algebra - Modulkategorie - Funktor - Nichtlineare Gleichung Differential equations, Nonlinear Frobenius algebras Modules (Algebra) Nichtlineare Gleichung (DE-588)4455337-7 gnd Funktor (DE-588)4130706-9 gnd Modulkategorie (DE-588)4170335-2 gnd Frobenius-Algebra (DE-588)4155476-0 gnd Separable Algebra (DE-588)4181009-0 gnd |
| subject_GND | (DE-588)4455337-7 (DE-588)4130706-9 (DE-588)4170335-2 (DE-588)4155476-0 (DE-588)4181009-0 |
| title | Frobenius and separable functors for generalized module categories and nonlinear equations |
| title_auth | Frobenius and separable functors for generalized module categories and nonlinear equations |
| title_exact_search | Frobenius and separable functors for generalized module categories and nonlinear equations |
| title_full | Frobenius and separable functors for generalized module categories and nonlinear equations Stefaan Caenepeel ; Gigel Militaru ; Shenglin Zhu |
| title_fullStr | Frobenius and separable functors for generalized module categories and nonlinear equations Stefaan Caenepeel ; Gigel Militaru ; Shenglin Zhu |
| title_full_unstemmed | Frobenius and separable functors for generalized module categories and nonlinear equations Stefaan Caenepeel ; Gigel Militaru ; Shenglin Zhu |
| title_short | Frobenius and separable functors for generalized module categories and nonlinear equations |
| title_sort | frobenius and separable functors for generalized module categories and nonlinear equations |
| topic | Separable Algebra - Frobenius-Algebra - Modulkategorie - Funktor - Nichtlineare Gleichung Differential equations, Nonlinear Frobenius algebras Modules (Algebra) Nichtlineare Gleichung (DE-588)4455337-7 gnd Funktor (DE-588)4130706-9 gnd Modulkategorie (DE-588)4170335-2 gnd Frobenius-Algebra (DE-588)4155476-0 gnd Separable Algebra (DE-588)4181009-0 gnd |
| topic_facet | Separable Algebra - Frobenius-Algebra - Modulkategorie - Funktor - Nichtlineare Gleichung Differential equations, Nonlinear Frobenius algebras Modules (Algebra) Nichtlineare Gleichung Funktor Modulkategorie Frobenius-Algebra Separable Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009823770&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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