偏π-余模的Maschke型定理.pdf

数 学 杂 志 Vo1．37(2017) J．ofMath．(PRC) NO．1 A M ASCHKE TYPE THE0REM F0R PARTIAL 7_r—C0M 0DULES JIA Ling ．CHEN Xiao—yuan (』．DepartmentofMathem。ties。ndStatistics，LudongUniversity，Yantai264025,China) (2．BasicDepartment，Zh~iangBusinessCollege，Hangzhou310053，China) Abstract：Inthispaper，westudytheMaschketypetheoremsofpartialgroup comodules． BythemethodsofweakHopfgroupcoalgebras，weobtaintheclassicalMaschketypetheoremsof Hopfalgebras，whichgeneralizedthoseofHopfalgebrasandresultsof[8】． Keywords： partial丌一comodule；tracemap；M aschketypetheorem 2010MR SubjectClassification： 16W30 Documentcode： A ArticleID： 0255—7797(2017)01—0021—07 1 Introduction Partialactionsofgroupsaspower~ltoolswereintroducedduringthestudyofoperator algebrasbyExel[2]．Withthefurtherdevelopment，manypositiveresultswereproposed [3-6]．CaenepeelandtheotherauthorsdevelopedatheoryofpartialactionsofHopfalgebras 1【]andintroducedthenotionofapartialentwiningstructureasageneralizationofentwining structure(see[9]) Onotherhand．thenotionofaHopf7r—coalgebrawhichgeneralizedthatofaHopfalgebra wasintroducedandplayedanimportantrole，consequentlygroup entwiningstructuresand groupweakentwiningstructurewerecarefullystudied．Motivatedbythisfact，weintroduce thenotionofapartialgroupcomoduleandgiveaM aschketypetheorem forthem．Because the “cOas8Ociativity”ofapartialstructureisdestroyed，thegeneralizationisnottrivialand easy． Inthispaper，wefirstrecallbasicdefinitionsofpartialgroupcomodulesandgivesome examples．Then westateaM aschke—typetheorem ofpartialgroup Hopfmoduleswhich generalizestherelevantresultsofHopfmodules(see[7，8])，entwinedmodules，groupHopf modules，etc．． Theorganization ofthepaperisasfollows：Firstweintroducethenotion