欢迎来到天天文库
浏览记录
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$aEq8FD(MoritaGE3V5=$;2$aES8l[0eEV^1eR(Artin;2)ErcotiltingaC?etiltingaEx=(A+$Tcotiltinga(`E=(MoritaxE3V51℄eR;2(Artin;2)Ercotiltingl tiltinglq0GzxV^
4、T1EVdiRcotilting
5、aSE!`iRcotiltinglAn2z6、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'-Ee+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'-Ee+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
此文档下载收益归作者所有