| Invariant properties of representations under cleft extensions |
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| 作者姓名： | Fang LI & Mian-mian ZHANG |
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| 作者单位： | Fang LI & Mian-mian ZHANG Department of Mathematics，Zhejiang University，Hangzhou，310027，China |
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| 基金项目： | 教育部新世纪优秀人才支持计划;国家自然科学基金 |
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| 摘 要： | The main aim of this paper is to give the invariant properties of representations of algebras under cleft extensions over a semisimple Hopf algebra. Firstly, we explain the concept of the cleft extension and give a relation between the cleft extension and the crossed product which is the approach we depend upon. Then, by making use of them, we prove that over an algebraically closed field k, for a finite dimensional Hopf algebra H which is semisimple as well as its dual H*, the representation type of an algebra is an invariant property under a finite dimensional H-cleft extension . In the other part, we still show that over an arbitrary field k, the Nakayama property of a k-algebra is also an invariant property under an H -cleft extension when the radical of the algebra is H-stable.
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| 收稿时间： | 18 November 2005 |
| 修稿时间： | 27 June 2006 |
Invariant properties of representations under cleft extensions |
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| Fang LI & Mian-mian ZHANG.Invariant properties of representations under cleft extensions[J].Science in China(Mathematics),2007,50(1):121-131. |
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| Authors: | Fang Li Mian-mian Zhang |
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| Institution: | Department of Mathematics, Zhejiang University, Hangzhou, 310027, China |
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| Abstract: | The main aim of this paper is to give the invariant properties of representations of algebras under cleft extensions over a semisimple Hopf algebra. Firstly, we explain the concept of the cleft extension and give a relation between the cleft extension and the crossed product which is the approach we depend upon. Then, by making use of them, we prove that over an algebraically closed field k, for a finite dimensional Hopf algebra H which is semisimple as well as its dual H*, the representation type of an algebra is an invariant property under a finite dimensional H-cleft extension . In the other part, we still show that over an arbitrary field k, the Nakayama property of a k-algebra is also an invariant property under an H -cleft extension when the radical of the algebra is H-stable. |
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| Keywords: | cleft extensions crossed product Nakayama algebra representation type |
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