Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations

Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu (auth.)3540437827, 9783540437826

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.

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Table of contents :
1. Generalities….Pages 3-37
2. Doi-Koppinen Hopf modules and entwined modules….Pages 39-87
3. Frobenius and separable functors for entwined modules….Pages 89-157
4. Applications….Pages 159-213
5. Yetter-Drinfeld modules and the quantum Yang-Baxter equation….Pages 217-243
6. Hopf modules and the pentagon equation….Pages 245-300
7. Long dimodules and the Long equation….Pages 301-316
8. The Frobenius-Separability equation….Pages 317-343
References….Pages 345-352
Index….Pages 353-354