简介:Inthispaper,westudynon-cosemisimpleHopfalgebrasthroughtheirunderlyingcoalgebrastructure.Weintroducetheconceptofthemaximalpointedsubcoalgebra/Hopfsubalgebra.Foranon-cosemisimpleHopfalgebraAwiththeChevalleyproperty,ifitsdiagramisaNicholsalgebra,thenthediagramofitsmaximalpointedHopfsubalgebraisalsoaNicholsalgebra.WhenAisoffinitedimension,weprovideanecessaryandsufficientconditionforA’sdiagramequalingthediagramofitsmaximalpointedHopfsubalgebra.
简介:LetHbeafinite-dimensionalweakHopfalgebraandAaleftH-modulealgebrawithitsinvariantsubalgebraA~H.WeprovethatthesmashproductA#HisanA-ringwithagrouplikecharacter,andgiveacriterionforA#HtobeFrobeniusoverA.UsingthetheoryofA-rings,wemainlyconstructaMoritacontextconnectingthesmashproductA#HandtheinvariantsubalgebraA~H,whichgeneralizesthecorrespondingresultsobtainedbyCohen,FischmanandMontgomery.
简介:从附加结构的角度将流形的多种概念有机地串联起来,并给出了一种直观理解流形、微分流形等抽象概念的新颖方式.同时,本文阐述了微分几何的主要特点、思想,介绍了与附加结构相关的流形分类问题、Poincare猜测等的研究情况.
简介:Thepurposeofthispaperistopresentsomedualpropertiesofdualcomodule.Itturnsoutthatdualcomodulehasuniversalproperty(cf.Theorem2).Since(()*,()°)isanadjointpair(cf.Theorem3),somenicepropertiesoffunctor()°areobtained.FinelyTheoram4providesthatthecotensorproductisthedualofthetensorproductby(MAN)°≌M°□A.N°.Moreover,theresultHomA(M,N)≌Coma.(N°,M°)isprovedforfiterelatedmodulesM,NoverarefiexivealgebraA.
简介:Inthispaper,westudyaYetter-DrinfeldmoduleVoveraweakHopfalgebraH.AlthoughthecategoryofallleftH-modulesisnotabraidedtensorcategory,wecandefineaYetter-Drinfeldmodule.UsingthisYetter-DrinfeldmodulesV,weconstructNicholsalgebraB(V)overtheweakHopfalgebraH,andaseriesofweakHopfalgebras.Someresultsof[8]aregeneralized.