TY  - BOOK
AU  - Caenepeel,Stefaan
AU  - Militaru,Gigel
AU  - Zhu,Shenglin
ED  - SpringerLink (Online service)
TI  - Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations
T2  - Lecture Notes in Mathematics,
SN  - 9783540480426
AV  - QA251.5 
U1  - 512.46 23
PY  - 2002///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Algebra
KW  - Associative Rings and Algebras
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/b83849
ER  -