| Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations 2002 Edition Contributor(s): Caenepeel, Stefaan (Author), Militaru, Gigel (Author), Zhu, Shenglin (Author) |
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ISBN: 3540437827 ISBN-13: 9783540437826 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: July 2002 Annotation: 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 expos?? 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Group Theory - Mathematics | Algebra - General - Mathematics | Algebra - Abstract |
| Dewey: 512.24 |
| LCCN: 2002070773 |
| Series: Lecture Notes in Mathematics |
| Physical Information: 0.77" H x 6.14" W x 9.21" (1.15 lbs) 354 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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 expos 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. |