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008 121227s2002 gw | s |||| 0|eng d
020 _a9783540480426
_9978-3-540-48042-6
024 7 _a10.1007/b83849
_2doi
050 4 _aQA251.5
072 7 _aPBF
_2bicssc
072 7 _aMAT002010
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512.46
_223
100 1 _aCaenepeel, Stefaan.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aFrobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations
_h[electronic resource] /
_cby Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2002.
300 _aXIV, 354 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1787
505 0 _aPart 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.
520 _aDoi-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.
650 0 _aAlgebra.
650 1 4 _aAssociative Rings and Algebras.
_0http://scigraph.springernature.com/things/product-market-codes/M11027
700 1 _aMilitaru, Gigel.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aZhu, Shenglin.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662170236
776 0 8 _iPrinted edition:
_z9783540437826
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1787
856 4 0 _uhttps://doi.org/10.1007/b83849
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c9365
_d9365