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- 2016
Hom-Yetter-Drinfeld模范畴的半单性
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Abstract:
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。
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
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