2、m*~~~~I~~~~~~~~A~~~'~B~~~~~~~~~tt~.::$:~W~~$~*~%~~*.A.ii~i.§.?Hopff:￠~1-?J&~{ffiij(~)itffl))**AifB±l-￥9f!iffi::k~lJ:1~1iffi±~1:fLM!'BJ,:ft~~m~~~~~~±~tt~~-*~~~~~~*~B±l~~m*~~~-*~~~~~~~~~~~~·tt~~~~*-*A~~7M~~~~*~*~*~~~ffi~~i1::~1￥J~J4lJ:E,!EJ~~&~OO#[P]{f*ffiHl~xit)CI￥J~EP14-*!l~-f~*'fti,Lfit:>c~i
3、iI~*of€H~.:$:fiJ:itUtfi￥ijrpW:::k~,QJ~*ffl~t:p~~1m~tUU.f.f&1*~itX,llJ~%Tf~$(it)(8{]1tg~￡V,t$7J"I*J~-fFir~~:-i:f#,~,B'Jj=vot'5it-6f48~-B:YiP~~:OtJ.-.~~BM=~s,b·K摘要Hopf?-余代數(shù)最初是由Turaev引入的一類代數(shù)結(jié)構(gòu),作為Hopf代數(shù)的一種推廣,Hopf?-余代數(shù)引起了廣大數(shù)學(xué)學(xué)者的研究興趣并被深入研究,經(jīng)過研究,Hopf代數(shù)上的許多重要結(jié)論在Hopf?-余代數(shù)上同樣是成立的.群的偏作用是由R.Exel所定義的一類特殊的
4、群作用,并且很快就成為了研究希爾伯特空間上部分等距生成的?*-代數(shù)的有效工具,并且隨著研究的深入,偏群作用已經(jīng)成為環(huán)論中的一個獨立且相當(dāng)重要的分支.本文基于以上背景,做了以下幾個方面的工作.首先我們給出了Hopf?-余代數(shù)的偏作用的定義,除此之外,我們還給出了偏Hopf?-余模等一系列的概念.在此之后,我們給出了偏?-?-余模張量積的概念,并證明兩個偏?-?-余模的張量積還是偏?-?-余模.最后,我們給出了偏?-smash積的定義,并嘗試構(gòu)造了一類Morita關(guān)系.關(guān)鍵詞:Hopf?-余代數(shù);Hopf?-余代數(shù)偏作用;偏?-?-余模;偏?-?????積.iAbstractHopf?
5、-coalgebraisanalgebraicstructureintroducedbythefamoustopologistTu-raev.AsanextendofHopfalgebra,Hopf?-coalgebradrawwideresearchattentionofmathematicianandisstudieddeeply,Afterresearch,ManyimportantconclusionsofHopfalgebraalsohasbeenprovedtoberightonHopf?-coalgebra.Partialactionofgroupisdefinedb
6、yR.Exelandsoonlybecomeaneffectivetoolintheresearchof?*-algebrasgeneratedbypartialisometriesontheHilbertspace.Withthedeepeningoftheresearch,partialgroupactionshasbecomeanindependentandimportantbranchofringtheory.Basedontheabovebackground.Inthispaper,wegiveaseriesofdefinationsofpartialHopf?-coac
7、tionandpartialHopf?-comoduleandsoon.Afterthat,wedefinedthepartial?-tensorproduct,andprovedthatapartial?-tensorproductoftwopartialHopf?-comodulealsoisapartialHopf?-comodule.Finally,wegiventheconceptofpartial?-smashproduct.Besides,wealsog
