Frobenius and separable functors for generalized module categories and nonlinear equations /

Frobenius and separable functors for generalized module categories and nonlinear equations /

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Bibliographic Details
Author / Creator:	Caenepeel, Stefaan, 1956-
Imprint:	Berlin ; New York : Springer, ©2002.
Description:	1 online resource (xiv, 354 pages).
Language:	English
Series:	Lecture notes in mathematics, 0075-8434 ; 1787 Lecture notes in mathematics (Springer-Verlag) ; 1787.
Subject:	Frobenius algebras. Modules (Algebra) Differential equations, Nonlinear. Differential equations, Nonlinear. Frobenius algebras. Modules (Algebra)
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11066122

Hidden Bibliographic Details
Varying Form of Title:	Frobenius and separable functors
Other authors / contributors:	Militaru, Gigel, 1966- Zhu, Shenglin, 1964-
ISBN:	3540437827 9783540437826 9783540480426 3540480420 9783764399979
Notes:	Includes bibliographical references (pages 345-352) and index.
Summary:	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.
Other form:	Print version: Caenepeel, Stefaan, 1956- Frobenius and separable functors for generalized module categories and nonlinear equations. Berlin ; New York : Springer, 2002

Description
Summary:	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.
Physical Description:	1 online resource (xiv, 354 pages).
Bibliography:	Includes bibliographical references (pages 345-352) and index.
ISBN:	3540437827 9783540437826 9783540480426 3540480420 9783764399979
ISSN:	0075-8434 ;