Yetter-Drinfeld范疇中的Hopf模余代數結構和H-cleft擴張.pdf

1、河南師范大學碩士學位論文YetterDrinfeld范疇中的Hopf模余代數結構和Hcleft擴張姓名：陳雙雙申請學位級別：碩士專業(yè)：基礎數學指導教師：趙文正20090401ABSTRACTInthispaper，wemainlyinvestigatetwoquestions：thefirstodeisHopfmodulecoalgebrasinYetter—DrinfeldcategoryThesecondoneisHcleftext

2、ensionsinYetterDrinfeldcategoryThedissertationisorganizedasfollows：Inthefirstchapter，weintroducethebackgroundofHopfalgebrasandpresentsomebasicpropertiesandthemotivationandmeaningofthisthesisareintroducedInthesecondchapte

3、r，firstly，werecallthedefinitionsinYetter—DrinfeldcategoryandmainlyweintroducethedefinitionofHopfmodulecoalgebra，Then，wegivethebasicstruc—turetheoremThatis：IfHisHopfalgebrainin2yDdefineYetter—DrinfeldcategoryBisrightH—Hop

4、fmodulecoalgebrainYetter—DrinfeldcategoryandleftB—rightHdoubleCOmoduleinYetter—Drinfeldcategory1etC=Bco日=blp(b)=b@1)，thenBisrightH—HopfmodulecoalgebrainYetter—DrinfeldandB竺CXHSubsequentlyweobtainHopfmodulecoalgebraissmas

5、hcoproductinYetter—DrinfeldcategoryInthethirdchapterwefirstlyrecallthedefinitionsandproperitiestheH—cleftextensionsinYetter—DrinfeldcategoryThen，weobtainthetheorem：letACBisH—cleftextensionsinYetter—DrinfeldcategoryWedefi

6、neha=∑7(‰)(^(2)1_n)，y。1(^(2)o)andaconvolutioninvertibleo(h，k)=∑7(^(1))7(^(2)_1一‰)7_1(危(2)o‰)ThenH、、‘，，，、、_，、‘，，J、、o，、_，，measuresanalgebraAinYetter—Drinfeldcategorywedefinecommutative(o@危)(6o夕)=∑a(hlh2—1h3—2_b)a(h2o，h3—1_

7、9(1))⑧h3o夕(2)Then44日竺B，AcBasH—cleftextensionsinYetterDrinfeldcategoryThatis：HcleftextensionsiscrossedproductinYetter—DrinfeldcategoryKEYWORDS：Hopfmodulecoalgebra，smashcoproduct，Yetter—Drinfeldcategorycleftextensions，cros