Cleft extensions of Koszul twisted Calabi–Yau algebras
Cleft extensions of Koszul twisted Calabi–Yau algebras
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DOI：
10.1007/s11856-016-1362-1
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发表时间：
2014-05
影响因子：
1
通讯作者：
Xiaolan Yu;F. van Oystaeyen;Yinhuo Zhang
中科院分区：
文献类型：
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作者：
Xiaolan Yu;F. van Oystaeyen;Yinhuo Zhang
讨论了一个扭曲的Calabi-Yau (CY) Hopf代数和h上的σ a 2环。设A为an - koszul扭曲CY代数，使其为h级σ-模代数。证明了裂推广也是一个扭曲的CY代数。这个结果有两个后果。首先，anN-Koszul扭曲CY代数与扭曲CY Hopf代数的粉碎积仍然是扭曲CY代数。其次，一个扭CY Hopf代数的裂对象都是扭CY代数。作为这一性质的应用，我们确定了Andruskiewitsch和Schneider引入的一类点Hopf代数u （D, λ）的裂对象是Calabi-Yau代数。
LetHbe a twisted Calabi–Yau (CY) Hopf algebra and σ a 2-cocycle onH. Let A be anN-Koszul twisted CY algebra such thatAis a gradedHσ- module algebra. We show that the cleft extensionA#σHis also a twisted CY algebra. This result has two consequences. Firstly, the smash product of anN-Koszul twisted CY algebra with a twisted CY Hopf algebra is still a twisted CY algebra. Secondly, the cleft objects of a twisted CY Hopf algebra are all twisted CY algebras. As an application of this property, we determine which cleft objects ofU(D, λ), a class of pointed Hopf algebras introduced by Andruskiewitsch and Schneider, are Calabi–Yau algebras.