| 广义Yetter—Drinfeld模上半单范畴的构造 |
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| 引用本文： | 张晓辉,王栓宏.广义Yetter—Drinfeld模上半单范畴的构造[J].东南大学学报,2013(4):467-469. |
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| 作者姓名： | 张晓辉 王栓宏 |
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| 作者单位： | 东南大学数学系,南京211189 |
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| 基金项目： | The National Natural Science Foundation of China （No. 11371088）, the Fundamental Research Funds for the Central Universities （No. 3207013906）, the Natural Science Foundation of Jiangsu Province （No. BK2012736）. |
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| 摘 要： | 设H是域k上的可换、诺特、半单、余半单的Hopf代数，且具有双射对极．考虑了其上YD（H）范畴的半单性，其中YD（H）是H上的广义Yetter—Drinfeld模范畴HYD^H（α，β）（其中α，β∈Autnopf（Hopf））的无交并．首先证明了YD（日）是一个对态射集封闭的范畴；然后利用有限生成投射模的性质和日的半单性，可得YD（H）是满足正合性条件的；进而由日是诺特、余半单的Hopf代数，得到YD（H）中的对象都可分解为单对象的直和．最终得到YD（H）是一个半单范畴．
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| 关 键 词： | 半单Hopf代数 半单范畴 广义Yetter—Drinfeld模 |
Construction of semisimple category over generalized Yetter-Drinfeld modules |
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| Zhang Xiaohui Wang Shuanhong.Construction of semisimple category over generalized Yetter-Drinfeld modules[J].Journal of Southeast University(English Edition),2013(4):467-469. |
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| Authors: | Zhang Xiaohui Wang Shuanhong |
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| Institution: | Zhang Xiaohui Wang Shuanhong (Department of Mathematics, Southeast University, Nanjing 211189, China) |
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| Abstract: | Let H be a commutative, noetherian, semisimple and cosemisimple Hopf algebra with a bijective antipode over a field k. Then the semisimplicity of YD（H） is considered, where YD （H） means the disjoint union of the category of generalized Yetter-Drinfeld modules nYD^H（ α, β） for any α, β E Aut Hopf（H）. First, the fact that YD（H） is closed under Mor is proved. Secondly, based on the properties of finitely generated projective modules and semisimplicity of H, YD（H） satisfies the exact condition. Thus each object in YD（H） can be decomposed into simple ones since H is noetherian and cosemisimple. Finally, it is proved that YD （H） is a sernisimple category. |
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| Keywords: | semisimple Hopf algebra semisimple category generalized Yetter-Drinfeld module |
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