拟Hopf代数上的模代数与交叉积及其推广.pdf

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8、µPureMathematicsFieldµHopfAlgebrasGradeµ2010NameµShixunLinSupervisorµAssociateProfessorBeishangRenAbstractQuasi-HopfalgebrasandquantumgroupsarenaturalgeneralizationofHopfalgebras.Nowadays,theyhavemanyremarkablepropertiesandcomewithaplentyofexamplesandapplicati

9、onsinpuremathematicsandmathematicalphysics.Inthispaper,wewillshowsomegeneralizeddenitionsandtheirproperties,andalsouseofmoduleactiontoresearchtherelationbetweenmodulealgebrasandthecrossedproductforquasi-Hopfalgebras.Wewillshowtherelevantresultsinthepaper.Inth

10、erstpartofthepaper(Chapter3),weresearchthemodulealgebraforquasi-Hopfalgebrasthroughmoduleactions.Weuseoftherightadjointactiona/gh=PgS(h1)ag(h2)foranya2A;h2Htoactonaunitalassociati