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- catalog abstract "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.".
- catalog alternative "Frobenius and separable functors".
- catalog contributor b12585175.
- catalog contributor b12585176.
- catalog contributor b12585177.
- catalog created "c2002.".
- catalog date "2002".
- catalog date "c2002.".
- catalog dateCopyrighted "c2002.".
- catalog description "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.".
- catalog description "Includes bibliographical references (p. [345]-352) and index.".
- catalog description "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.".
- catalog extent "xiv, 354 p. ;".
- catalog hasFormat "Also available in an electronic version.".
- catalog identifier "3540437827 (pbk. : acid-free paper)".
- catalog isFormatOf "Also available in an electronic version.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1787.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1787".
- catalog issued "2002".
- catalog issued "c2002.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer,".
- catalog relation "Also available in an electronic version.".
- catalog subject "510 s 512/.24 21".
- catalog subject "Algebra.".
- catalog subject "Differential equations, Nonlinear.".
- catalog subject "Frobenius algebras.".
- catalog subject "Mathematics.".
- catalog subject "Modules (Algebra)".
- catalog subject "QA3 .L28 no. 1787 QA251.5".
- catalog tableOfContents "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.".
- catalog title "Frobenius and separable functors for generalized module categories and nonlinear equations / Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu.".
- catalog title "Frobenius and separable functors".
- catalog type "Computer network resources. local".
- catalog type "Electronic books. lcsh".
- catalog type "text".