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ID：37125181
大小：1.87 MB
页数：38页
时间：2019-05-18
《高维cotilting模诱导的子范畴对偶》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。
1、上海交通大学硕士学位论文高维cotilting模诱导的子范畴对偶姓名：李志伟申请学位级别：硕士专业：基础数学指导教师：章璞20061201{'G:
2、5%
3、UaVTiltinga(;2$aEq8FD(MoritaG E3V5=$;2$aES8l [0eEV^1 eR(Artin;2)ErcotiltingaC?etiltingaEx=(A+$Tcotiltinga( ` E=(MoritaxE3V51℄ eR;2(Artin;2)Ercotiltingl tiltingl q0GzxV^
4、T1EVdiRcotilting
5、aSE!`iRcotiltinglA n2z6、ExtAei(Y,T)=0,∀i≥0,i6=e}TB={YB∈m7、od-B8、ExtBeeee3ExtA(−,T)9、ATe:AT→TB(lx}{r}ExtB(−,T)10、Te:BTe→TeBA1-y' -E e+lZ0(+TEXdS1iRcotiltingln2ZVd[AR]a5.10ElA+>iVEIVÆT∈A-mod(r-cotiltingl3χT1A-mod(} eEwr-cotiltinglxZ0r9}r-cotilting} eZ0i{'G:11、5%12、UaVABSTRACTTiltingtheoryisacentraltopicintherepresentati13、ontheoryoffinitedi-mensional(Artinalgebra).ItcanbeseenthegeneralizationofMoritaEquiv-alenceandhasextensiveinteractionwithvariousresearchdirectionsinrepre-sentationtheory.Cotiltingtheorycanbeseenasthedualityoftiltingtheoryinfinitedimensionalalgebra.Itisusefultogivethecotiltingtheorydirectly.Wecanno14、tgetthecotiltingmodulesbydualityingeneralcase,andasthemainpartsofhigherdimensionalcotiltingtheory,thebasictheoremsofhigherdimensionalcotiltingmoduleshavenotbeenstatedconcretelyinpreviouspa-pers.InthispaperWegivethebasictheoremsofhigherdimensionalcotiltingmodulesdirectly,theyarethefollowings(Abea15、finitedimensionalalgebraoverafieldk):1LetT∈A-modbear-cotiltingmoduleB=End(T)op,thenwehaveA(i)TBisalsoar-cotiltingmodule.(ii)A∼=EndB(TB),a7→(t7→at),a∈A,t∈T.2LetT∈A-modbear-cotiltingmoduleB=End(T)op,0≤e≤rbeAaninteger.WedenoteTe={X∈A-mod16、Exti(X,T)=0,∀i≥0,i6=e}AAAandTe={Y∈mod-B17、Exti(Y,T)=0,∀i≥0,i6=e}.18、BBBeeethenwehaveExtA(−,T)19、ATe:AT→TBisadualityfunctoranditsinverseeeefunctorisExtB(−,T)20、Te:TB→AT.BInfacttheabovetheoremsarerightinthefinitegeneratedmodulecategoriesofarbitraryassociaterings.Byusingtheprevioustheorems,Wegiveand
6、ExtAei(Y,T)=0,∀i≥0,i6=e}TB={YB∈m
7、od-B
8、ExtBeeee3ExtA(−,T)
9、ATe:AT→TB(lx}{r}ExtB(−,T)
10、Te:BTe→TeBA1-y' -E e+lZ0(+TEXdS1iRcotiltingln2ZVd[AR]a5.10ElA+>iVEIVÆT∈A-mod(r-cotiltingl3χT1A-mod(} eEwr-cotiltinglxZ0r9}r-cotilting} eZ0i{'G:
11、5%
12、UaVABSTRACTTiltingtheoryisacentraltopicintherepresentati
13、ontheoryoffinitedi-mensional(Artinalgebra).ItcanbeseenthegeneralizationofMoritaEquiv-alenceandhasextensiveinteractionwithvariousresearchdirectionsinrepre-sentationtheory.Cotiltingtheorycanbeseenasthedualityoftiltingtheoryinfinitedimensionalalgebra.Itisusefultogivethecotiltingtheorydirectly.Wecanno
14、tgetthecotiltingmodulesbydualityingeneralcase,andasthemainpartsofhigherdimensionalcotiltingtheory,thebasictheoremsofhigherdimensionalcotiltingmoduleshavenotbeenstatedconcretelyinpreviouspa-pers.InthispaperWegivethebasictheoremsofhigherdimensionalcotiltingmodulesdirectly,theyarethefollowings(Abea
15、finitedimensionalalgebraoverafieldk):1LetT∈A-modbear-cotiltingmoduleB=End(T)op,thenwehaveA(i)TBisalsoar-cotiltingmodule.(ii)A∼=EndB(TB),a7→(t7→at),a∈A,t∈T.2LetT∈A-modbear-cotiltingmoduleB=End(T)op,0≤e≤rbeAaninteger.WedenoteTe={X∈A-mod
16、Exti(X,T)=0,∀i≥0,i6=e}AAAandTe={Y∈mod-B
17、Exti(Y,T)=0,∀i≥0,i6=e}.
18、BBBeeethenwehaveExtA(−,T)
19、ATe:AT→TBisadualityfunctoranditsinverseeeefunctorisExtB(−,T)
20、Te:TB→AT.BInfacttheabovetheoremsarerightinthefinitegeneratedmodulecategoriesofarbitraryassociaterings.Byusingtheprevioustheorems,Wegiveand
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