Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations

Download or read book Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations written by Stefaan Caenepeel and published by Springer. This book was released on 2004-10-13 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.