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1、JournalofAlgebra321(2009)3816–3826ContentslistsavailableatScienceDirectJournalofAlgebrawww.elsevier.com/locate/jalgebraCoveringfunctorswithoutgroups✩JoséA.delaPeñaa,MaríaJuliaRedondob,∗aInstitutodeMatemáticas,UNAM.Cd.Universitaria,México04510DF,MexicobDepartamentodeMatemática,UniversidadNacionalde
2、lSur,8000,BahíaBlanca,ArgentinaarticleinfoabstractArticlehistory:CoveringsintherepresentationtheoryofalgebraswereintroducedReceived30March2008fortheAuslander–Reitenquiverofarepresentation-finitealgebraAvailableonline7April2009in[Ch.Riedtmann,Algebren,Darstellungsköcher,ÜberlagerungenCommunicatedbyM
3、ichelVandenBerghundzurüch,Comment.Math.Helv.55(1980)199–224]andlaterforfinite-dimensionalalgebrasin[K.Bongartz,P.Gabriel,CoveringKeywords:spacesinrepresentationtheory,Invent.Math.65(3)(1982)331–CoveringsRepresentationtype378;P.Gabriel,Theuniversalcoverofarepresentation-finitealgebra,in:Proc.Represen
4、tationTheoryI,Puebla,1980,in:LectureNotesinMath.,vol.903,Springer,1981,pp.68–105;R.Martínez-Villa,J.A.delaPeña,Theuniversalcoverofaquiverwithrelations,J.PureAppl.Algebra30(3)(1983)277–292].ThebestunderstoodclassofcoveringfunctorsisthatofGaloiscoveringfunctorsF:A→Bdeterminedbytheactionofagroupofaut
5、omorphismsofA.InthisworkweintroducethebalancedcoveringfunctorswhichincludetheGaloisclassandforwhichclassicalGaloiscovering-typeresultsstillhold.Forinstance,ifF:A→Bisabalancedcoveringfunctor,whereAandBarelinearcategoriesoveranalgebraicallyclosedfield,andBistame,thenAistame.©2009ElsevierInc.Allrights
6、reserved.IntroductionandnotationLetkbeafieldandAbeafinite-dimensional(associativewith1)k-algebra.Oneofthemaingoalsoftherepresentationtheoryofalgebrasisthedescriptionofthecategoryoffinite-dimensionalleftmodulesAmod.ForthatpurposeitisimportanttodeterminetherepresentationtypeofA.Thefiniterepresentationty
7、pe(thatis,whenAacceptsonlyfinitelymanyindecomposableobjectsinAmod,✩TheresearchforthispaperwasinitiatedduringavisitofthesecondnamedauthortoUNAM,México.*Correspondingauthor.E-mailaddresses:jap@matem.unam.mx(J.A.dela