| 单的模代数及其稳定化子 |
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| 引用本文： | 王彩虹,赵利辉.单的模代数及其稳定化子[J].纯粹数学与应用数学,2014(1):27-31. |
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| 作者姓名： | 王彩虹 赵利辉 |
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| 作者单位： | [1] 河南理工大学数学与信息科学学院,河南 焦作454000 [2] 河南科技大学数学与统计学院,河南 洛阳471023 |
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| 基金项目： | 国家自然科学基金（11101128,11301155）;河南省教育厅自然科学基金（128110008）;河南省高等学校青年骨干教师资助计划项目（2012GGJS-061）. |
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| 摘 要： | 研究了有限维Hopf代数H与其单的模代数A的smash积的结构.通过给出A的反代数与其极小左理想的稳定化子的结构,证明了H与A的smash积与某个代数上的全矩阵代数是代数同构的,推广了以往的结果.
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| 关 键 词： | Hopf代数 smash积 单的模代数 全矩阵代数 |
On simple module algebra and its stabilizer |
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| Wang Caihong,Zhao Lihui.On simple module algebra and its stabilizer[J].Pure and Applied Mathematics,2014(1):27-31. |
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| Authors: | Wang Caihong Zhao Lihui |
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| Institution: | School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China; 2. School of Mathematics and Statistics, Henan University of Science and Technology Luoyang 471023, China) |
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| Abstract: | In this paper, the structure of the smash product of a finite-dimensional Hopf algebra H and its simple module algebra A is studied. By giving the structure of the stabilizer of the opposite algebra of A and its minimal left ideal, it is proved that, the smash product of H and A is algebraically isomorphic to a full matrix algebra over some algebra. The work generalizes the previous conclusions. |
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| Keywords: | Hopf algebra smash product simple module algebra full matrix algebra |
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