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,2000,43(3):457-462. |
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作者姓名: | 姜小龙 许永华 |
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作者单位: | [1]中山大学数学系 [2]复旦大学数学所 |
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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 |
修稿时间: | : |
On the Isomorphic Classes of Hopf-Galois Extensions with Normal Bases over a Commutative Ring |
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Institution: | JIANG Xiao-long (Department of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China) XU Yong-hua (Institute of Mathematics, Fadal University, Guangzhou 510275, P. R. China) |
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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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