| 素特征域上广义Witt李超代数的自同构群 |
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| 引用本文： | 刘文德,张永正.素特征域上广义Witt李超代数的自同构群[J].数学学报,2004,47(6):1123-113. |
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| 作者姓名： | 刘文德 张永正 |
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| 作者单位： | 1. 东北师范大学数学系,长春,130024;哈尔滨师范大学数学系,哈尔滨,150080
2. 哈尔滨师范大学数学系,哈尔滨,150080 |
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| 基金项目： | 国家自然科学基金资助项目(10271076)，教育部科技重点资助项目(99036) |
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| 摘 要： | 设W是素特征域上无限维或有限维广义Witt李超代数.本文利用W的自然滤过不变性和W的底代数的不变维数性质,证明了W的自同构群AutW同构于W的底代数的容许自同构群,还证明了在此群同构之下,AutW的标准正规列恰好对应W的底代数的容许自同构群的标准正规列,并给出AutW若干较为细致的性质.
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| 关 键 词： | 广义Witt李超代数 自同构群 自然滤过 |
| 文章编号： | 0583-1431(2004)06-1123-10 |
The Automorphism Groups of Generalized Witt Lie Superalgebras over a Field of Prime Characteristic |
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| Wen De LIU.The Automorphism Groups of Generalized Witt Lie Superalgebras over a Field of Prime Characteristic[J].Acta Mathematica Sinica,2004,47(6):1123-113. |
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| Authors: | Wen De LIU |
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| Institution: | Wen De LIU
(Department of Mathematics, Northeast Normal University, Changchun 130024, P. R. China) (Department of Mathematics, Harbin Normal University, Harbin 150080, P. R. China) Yong Zheng ZHANG (Department of Mathematics, Harbin Normal University, Harbin 150080, P. R. China) |
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| Abstract: | Let W be the infinite-dimensional or finite-dimensional generalized Witt Lie superalgebra over a field of prime characteristic and Aut W the automorphism group. Employing the invariance of the natural filtration of W and the invariant dimension property of the base algebra of W, we prove that Aut W is isomorphic to the admissible automorphism group of the base algebra of W. Then it is proved that the group isomorphism sends the standard normal series of Aut W to the one of the admissible automorphism groups, and further properties of Aut W are given. |
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| Keywords: | Generalized Witt Lie superalgebras Automorphism groups Natural filtra-tions |
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