Hopf代数与弱Hopf代数上的余模结构

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5、aandWeakHopfAlgebraMajor:PureMathematicsName:HaiyanXuSupervisor:ProfessorBeishangRenAbstractThenotionofaHopfalgebrawasdevelopedbyalgebraictopologistsabstractingtheworkofH.Hopfonmanifoldsin1941.Startingwithissueofthearticle”OnthestructureofHopfalgebras”,writ

6、tenbyJ.MilnorandJ.Moorein1965,Hopfalgebrasbecameasubjectofstudyfromastrictlyalgebraicpointofview.Bytheendofthe1990s,researchinthisfieldwasgivenastrongboostbytheappearanceofquantumgroupsandthedevelopmentoftheactiontheoryofHopfalgebraswhichunifiesearlierresults

7、knownforgroupactions,actionsofLiealgebras,andgradedrings.Sincethe1990s,thereappearmanyHopfalgebraicconstructions,suchasweakHopfalgebra,quasi-Hopfalgebra,Hopfcoalgebraandsoon.WeakHopfalgebrashavebeenproposedbyG.Bohm,K.Szlachanyifirst,itisthepromotionofHopfalg

8、ebra.WeakHopfalgebrahasstrictmathematicalandphysicalbackground,Suchassurfacealgebra,QuantumgroupandsoonarealltheexampleofweakHopfalgebra.Inrecentyears,weakHopfalgebraobtainedgreatachievementswhichattractedmoreattentionofmathematicians.Thismakesthedevelopmen

9、tofweakHopfalgebraisparticularlyfast,comparedwithotherHopfalgebraisconcerned,weakHopfalgebraisacoassociativealgebra.ThisenablesustodefinecoactionasHopfalgebradoes.Thispaperaredividedintothreechapters.Th