%0 Journal Article
%T Hom-Yetter-Drinfeld模范畴的半单性<br>Semisimplicity of the categories of Hom-Yetter-Drinfeld modules
%A 郭双建
%A 李怡铮&lt
%A br&gt
%A GUO Shuang-jian
%A LI Yi-zheng
%J 山东大学学报（理学版）
%D 2016
%R 10.6040/j.issn.1671-9352.0.2016.112
%X 摘要： 设k是域,(H,α)是带有双射对极的monoidal Hom-Hopf代数, 如果(H,α)是交换的, 诺特的, 半单和余半单, 则Hom-Yetter-Drinfeld模范畴HHYD H是半单的。也就是说设(H,α)是交换的monoidal Hom-Hopf代数。 假设HHYD H 满足某一条件, 并且函子(-)coH:HHYD H→H(Mk)是正合的。 如果(M, μ)∈HHYD H 作为左(H,α)-模是有限生成的, 则(M,μ)∈HHYD H 保持对象。<br>Abstract: Let k be a field, and(H,α)a monoidal Hom-Hopf algebra with bijective antipode. If(H,α)is commutative, noetherian, semisimple and cosemisimple, then the category HHYD H of Hom-Yetter-Drinfeld modules is semisimple. That is Let(H,α)be commutative. Assume that HHYD H satisfies some condition, and that the functor(-)coH:HHYD H→H(Mk)is exact. If (M,μ)∈HHYD H is finitely generated as an(H,α)-module, then (M,μ) is a projective object in HHYD H
%K Hom-Yetter-Drinfeld模
%K 半单
%K 诺特
%K 交换
%K monoidal Hom-Hopf代数
%K &lt
%K br&gt
%K noetherian
%K Hom-Yetter-Drinfeld modules
%K semisimple
%K commutation
%K monoidal Hom-Hopf algebras
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2016.112