Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations

1. Front Matter

   Pages I-XIV

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2. 1. Generalities

   • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu

   Pages 3-37

3. 2. Doi-Koppinen Hopf modules and entwined modules

   • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu

   Pages 39-87

4. 3. Frobenius and separable functors for entwined modules

   • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu

   Pages 89-157

5. 4. Applications

   • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu

   Pages 159-213

6. 5. Yetter-Drinfeld modules and the quantum Yang-Baxter equation

   • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu

   Pages 217-243

7. 6. Hopf modules and the pentagon equation

   • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu

   Pages 245-300

8. 7. Long dimodules and the Long equation

   • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu

   Pages 301-316

9. 8. The Frobenius-Separability equation

   • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu

   Pages 317-343

10. References

    • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu

    Pages 345-352

11. Index

    • Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu

    Pages 353-354

12. Back Matter

    Pages 355-355

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Doi-Koppinen Hopf modules and entwined modules unify various kinds of modules that have been intensively studied over the past decades, such as Hopf modules, graded modules, Yetter-Drinfeld modules. The book presents a unified theory, with focus on categorical concepts generalizing the notions of separable and Frobenius algebras, and discussing relations with smash products, Galois theory and descent theory. Each chapter of Part II is devoted to a particular nonlinear equation. The exposé is organized in such a way that the analogies between the four are clear: the quantum Yang-Baxter equation is related to Yetter-Drinfeld modules, the pentagon equation to Hopf modules, and the Long equation to Long dimodules. The Frobenius-separability equation provides a new viewpoint to Frobenius and separable algebras.

• Entwined module
• Frobenius functor
• Galois theory
• Nonlinear equation
• Separable functor
• Yetter-Drinfeld module
• algebra
• equation

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