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1、LecturesonRepresentationsofQuiversbyWilliamCrawley-BoeveyContents§1.Pathalgebras......................3§2.Bricks.........................9§3.Thevarietyofrepresentations.............11§4.DynkinandEuclideandiagrams..............15§5.Finiterepresentation
2、type...............19§6.Morehomologicalalgebra................21§7.Euclideancase.Preprojectivesandpreinjectives....25§8.Euclideancase.Regularmodules.............28§9.Euclideancase.Regularsimplesandroots........32§10.Furthertopics.....................3
3、61A'quiver'isadirectedgraph,andarepresentationisdefinedbyavectorspaceforeachvertexandalinearmapforeacharrow.Thetheoryofrepresentationsofquiverstoucheslinearalgebra,invarianttheory,finitedimensionalalgebras,freeidealrings,Kac-MoodyLiealgebras,andmanyot
4、herfields.ThesearethenotesforacourseofeightlecturesgiveninOxfordinspring1992.Myaimwastheclassificationoftherepresentationsforthe~~~~~EuclideandiagramsA,D,E,E,E.Itseemedambitiousforeightnn678lectures,butturnedouttobeeasierthanIexpected.TheDynkincaseisa
5、nalysedusinganargumentofJ.Tits,P.GabrielandC.M.Ringel,whichinvolvesactionsofalgebraicgroups,astudyofrootsystems,andsomecleverhomologicalalgebra.TheEuclideancaseistreatedusingthesametools,andinadditiontheAuslander-Reitentranslations-
