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1、A.I.KostrikinI.R.Shafarevich(Eds.)AlgebraVIIIRepresentationsofFinite-DimensionalAlgebrasWith98FiguresSpringer-VerlagBerlinHeidelbergNewYorkLondonParisTokyoHongKongBarcelonaBudapestEncyclopaediaofMathematicalSciencesVolume73Editor-in-Chief:R.V.GamkrelidzeRepresentationsofFinite-DimensionalAlgebra
2、sP.Gabriel,A.V.RoiterContentsForeword21.MatrixProblems42.Algebras,ModulesandCategories153.Radical,Decomposition,Aggregates254.FinitelySpacedModules335.FinitelyRepresentedPosets466.Roots567.RepresentationsofQuivers628.Spectroids,Quivers,Coherence739.AlmostSplitSequences8710.PostprojectiveComponen
3、ts10111.RepresentationsofTameQuivers12012.DerivationandTilting(byB.Keller)13013.MultiplicativeBases14214.FinitelyRepresentedAlgebras156Bibliography166SubjectIndex173ListofSymbols176ForewordThismonographaimsatageneraloutlineofoldandnewresultsonrepresentationsoffinite-dimensionalalgebras.Inatheory
4、whichdevelopedrapidlyduringthelasttwodecades,thelackoftextbooksisthemainimpedimentfornovices.Wethereforepaidspecialattentiontothefoundationsandincludedproofsforstatementswhichareelementary,servecomprehensionorarescarcelyavailable.Inthismannerwetrytoleadthereaderuptoapointwherehecanfindhiswayinth
5、eoriginalliterature.Theboundsimposeduponthevolumepreventusfromendeavouringaftercompleteness.Thuswecenteredthediscourseroundthefairlycompletetheoryoffinitelyrepresentedalgebras,onlytouchingtamedenizensandomittingforinstancequestionsofdegeneration,bocses,Riedtmann'sinvestigationofself-injectivealg
6、ebras....FirstexamplesofproblemsandanintroductiontoterminologyarepresentedintheSect.1and2,whichshouldbeaccessibleto"everybody".ReaderssearchingforadeeperinsightmaylookatSect.3and7,whichstillareintroductory.Tocompletethissketchyview,weincludedan"organigram"andproposeashortbibliographywhichpointst
7、ocharacteristicrepresentativesofthemainbranchesofdevelopmentandconsistsofthereferences[108],[62],[134],[79],[52],[63],[110],[91],[19],[39],[57],[8],[129],[119],[81],[126],[43],[32],[34],[115],[22],[14],[132],[12],[26],[5],[4
