Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations

Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu (Autoren)

Buch | Softcover

XIV, 354 Seiten

2002 | 2002
Springer Berlin (Verlag)
978-3-540-43782-6 (ISBN)

Artikel merken

Doi-Koppinen Hopf modules and entwined modules unify various kinds of modules that have been intensively studied over the pastdecades, 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.

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.

Erscheint lt. Verlag	23.7.2002
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XIV, 354 p.
Verlagsort	Berlin
Sprache	englisch
Maße	152 x 229 mm
Gewicht	560 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Schlagworte	Algebra • Entwined module • Equation • Frobenius functor • Galois Theory • Nonlinear equation • Separable functor • Yetter-Drinfeld module
ISBN-10	3-540-43782-7 / 3540437827
ISBN-13	978-3-540-43782-6 / 9783540437826
Zustand	Neuware