Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations

• Main Authors: Caenepeel, Stefaan (Author, http://id.loc.gov/vocabulary/relators/aut), Militaru, Gigel (http://id.loc.gov/vocabulary/relators/aut), Zhu, Shenglin (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
• Edition: 1st ed. 2002.
• Series: Lecture Notes in Mathematics, 1787
• Subjects: Associative rings.; Rings (Algebra).; Associative Rings and Algebras.
• Physical Description: XIV, 354 p. online resource.
• ISBN: 9783540480426
• ISSN: 0075-8434 ;
• DOI: 10.1007/b83849

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.