Frobenius and separable functors for generalized module categories and nonlinear equations /
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| Author / Creator: | Caenepeel, Stefaan, 1956- |
|---|---|
| Imprint: | Berlin ; New York : Springer, 2002. |
| Description: | 1 online resource (xiv, 343 p.) |
| Language: | English |
| Series: | Lecture notes in mathematics, 0075-8434 ; 1787 Lecture notes in mathematics (Springer-Verlag) ; 1787. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/8866642 |
Table of Contents:
- Part I. Entwined modules and Doi-Koppinen Hopf modules
- 1. Generalities
- 1.1. Coalgebras, bialgebras, and Hopf algebras
- 1.2. Adjoint functors
- 1.3. Separable algebras and Frobenius algebras
- 2. Doi-Koppinen Hopf modules and entwined modules
- 2.1. Doi-Koppinen structures and entwining structures
- 2.2. Doi-Koppinen modules and entwined modules
- 2.3. Entwined modules and the smash product
- 2.4. Entwined modules and the smash coproduct
- 2.5. Adjoint functors for entwined modules
- 2.6. Two-sided entwined modules
- 2.7. Entwined modules and comodules over a coring
- 2.8. Monoidal categories
- 3. Frobenius and separable functors for entwined modules
- 3.1. Separable functors and Frobenius functors
- 3.2. Restriction of scalars and the smash product
- 3.3. The functor forgetting the C-coaction
- 3.4. The functor forgetting the A-action
- 3.5. The general induction functor
- 4. Applications
- 4.1. Relative Hopf modules
- 4.2. Hopf-Galois extensions
- 4.3. DoiÆs [H,C]-modules
- 4.4. Yetter-Drinfeld modules
- 4.5. Long dimodules
- 4.6. Modules graded by G-sets
- 4.7. Two-sided entwined modules revisited
- 4.8. Corings and descent theory
- Part II. Nonlinear equations
- 5. Yetter-Drinfeld modules and the quantum Yang-Baxter equation
- 5.1. Notation
- 5.2. The quantum Yang-Baxter equation and the braid equation
- 5.3. Hopf algebras versus the QYBE
- 5.4. The FRT Theorem
- 5.5. The set-theoretic braid equation
- 6. Hopf modules and the pentagon equation
- 6.1. The Hopf equation and the pentagon equation
- 6.2. The FRT Theorem for the Hopf equation
- 6.3. New examples of noncommutative noncocommutative bialgebras
- 6.4. The pentagon equation versus the structure and the classification of finite dimensional Hopf algebras
- 7. Long dimodules and the Long equation
- 7.1. The Long equation
- 7.2. The FRT Theorem for the Long equation
- 7.3. Long coalgebras
- 8. The Frobenius-Separability equation
- 8.1. Frobenius algebras and separable algebras
- 8.2. The Frobenius-separability equation
- 8.3. The structure of Frobenius algebras and separable algebras
- 8.4. The category of FS-objects
- References
- Index