Frobenius and separable functors for generalized module categories and nonlinear equations / Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1787Langue : anglais.Éditeur : Berlin : Springer, 2002ISBN: 9783540437826.ISSN: 1617-9692.Sujet MSC : 16D90, Modules, bimodules and ideals in associative algebras, Module categories in associative algebras; module theory in a category-theoretic context; Morita equivalence and duality16Txx, Associative rings and algebras - Hopf algebras, quantum groups and related topics
16S40, Associative rings and algebras arising under various constructions, Smash products of general Hopf actions
16W50, Associative rings and algebras with additional structure, Graded rings and modules
16B50, General and miscellaneous, Category-theoretic methods and results in associative algebrasEn-ligne : Springerlink | Zentralblatt | MathSciNet
... The chapters of Part I are the following: 1. Generalities. 2. Doi-Koppinen Hopf modules and entwined modules. 3. Frobenius and separable functors for entwined modules. 4. Applications. ... The chapters of the second Part are: 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.
The authors start with elementary facts about coalgebras, Hopf algebras and their actions and coactions, adjoint functors, separable algebras, Frobenius algebras, etc., and they reach to advanced results, providing complete proofs and a large number of examples. There is a comprehensive bibliography at the end of the book. Many of the results in the book represent the contribution of the authors to the field. The book can be used by people working in the area, but it is also a good introductory text for graduate students. (Zentralblatt)
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