| 关于交换环上带正则基的Hopf-Galois扩张的同构类 |
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| 引用本文： | 姜小龙,许永华.关于交换环上带正则基的Hopf-Galois扩张的同构类[J].数学学报,2000(3). |
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| 作者姓名： | 姜小龙 许永华 |
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| 作者单位： | 中山大学数学系!广东广州510275(姜小龙)，复旦大学数学所!上海200433(许永华) |
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| 基金项目： | 国家自然科学基金!（19771090） |
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| 摘 要： | 本文考虑交换环上带正则基的Ｈｏｐｆ－Ｇａｌｏｉｓ扩张的刻划及其同构类集合的结 构．主要结论是：当Ｂ为一交换环、Ｈ为余交换的有限Ｈｏｐｆ时，上述同构类集合 构成群并与 Ｌ~＊＝（ＢＨ）~＊的 ２次上同调群 Ｈ~２（Ｌ~＊， Ｕ）同构．
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| 关 键 词： | Hopf-Galois扩张 正则基 |
On the Isomorphic Classes of Hopf-Galois Extensions with Normal Bases over a Commutative Ring |
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| JIANG Xiao-long.On the Isomorphic Classes of Hopf-Galois Extensions with Normal Bases over a Commutative Ring[J].Acta Mathematica Sinica,2000(3). |
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| Authors: | JIANG Xiao-long |
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| Abstract: | In this paper, we consider the isomorphic classes of H-Galois extensions with the normal basis property over a fixed comutative ring B for a finite Hopf algebra H. The result is that when H is cocommutative, then the above isomorphic classes and the 2-th cohomology group. H~2(L~*, U) are isomorphic as groups under the product defined in this paper, where L=B H, L~* == Hom_B(L, B). |
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| Keywords: | Hopf-Galois extensions Cohomology group |
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