03579nam 22006375 450 991014494170332120200703234738.03-540-48042-010.1007/b83849(CKB)1000000000233268(SSID)ssj0000323306(PQKBManifestationID)12132003(PQKBTitleCode)TC0000323306(PQKBWorkID)10297162(PQKB)10266875(DE-He213)978-3-540-48042-6(MiAaPQ)EBC6301255(MiAaPQ)EBC5585683(Au-PeEL)EBL5585683(OCoLC)1066179141(PPN)155170910(EXLCZ)99100000000023326820121227d2002 u| 0engurnn|008mamaatxtccrFrobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations /by Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu1st ed. 2002.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2002.1 online resource (XIV, 354 p.) Lecture Notes in Mathematics,0075-8434 ;1787Bibliographic Level Mode of Issuance: Monograph3-540-43782-7 Includes bibliographical references (pages [345]-352) and index.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.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.Lecture Notes in Mathematics,0075-8434 ;1787Associative ringsRings (Algebra)Associative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11027Associative rings.Rings (Algebra).Associative Rings and Algebras.512.24Caenepeel Stefaanauthttp://id.loc.gov/vocabulary/relators/aut59359Militaru Gigelauthttp://id.loc.gov/vocabulary/relators/autZhu Shenglinauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910144941703321Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations2528850UNINA