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＜E-Book＞
Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations / by Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
(Lecture Notes in Mathematics. ISSN:16179692 ; 1787)

Edition	1st ed. 2002.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2002
Language	English
Size	XIV, 354 p : online resource
Authors	*Caenepeel, Stefaan author Militaru, Gigel author Zhu, Shenglin author SpringerLink (Online service)
Subjects	LCSH:Associative rings LCSH:Associative algebras FREE:Associative Rings and Algebras
Notes	Part I: Entwined modules and Doi-Koppinen Hopf modules -- 1. Generalities -- 2. Doi-Koppinen Hopf modules and entwined modules -- 3. Frobenius and separable functors for entwined modules -- 4. Applications -- Part II: Nonlinear equations -- 5. Yetter-Drinfeld modules and the quantum Yang-Baxter equation -- 6. Hopf modules and the pentagon equation -- 7. Long dimodules and the Long equation -- 8. The Frobenius-Separability equation -- References -- Index 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 HTTP:URL=https://doi.org/10.1007/b83849

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