简介:Inthispaper,westudynon-cosemisimpleHopfalgebrasthroughtheirunderlyingcoalgebrastructure.Weintroducetheconceptofthemaximalpointedsubcoalgebra/Hopfsubalgebra.Foranon-cosemisimpleHopfalgebraAwiththeChevalleyproperty,ifitsdiagramisaNicholsalgebra,thenthediagramofitsmaximalpointedHopfsubalgebraisalsoaNicholsalgebra.WhenAisoffinitedimension,weprovideanecessaryandsufficientconditionforA’sdiagramequalingthediagramofitsmaximalpointedHopfsubalgebra.