| 限制李超代数的环面秩 |
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| 引用本文： | 孙丽萍,刘文德.限制李超代数的环面秩[J].数学学报,2021,64(1):167-176. |
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| 作者姓名： | 孙丽萍 刘文德 |
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| 作者单位： | 1.哈尔滨理工大学理学院 哈尔滨 150080;2.海南师范大学数学与统计学院 海口 571158 |
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| 基金项目： | 国家自然科学基金资助（11471090）；黑龙江省自然科学基金资助（A2015017，QC2018006） |
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| 摘 要： | 本文将模李代数中环面与环面秩的理论推广到模李超代数中.应用模李超代数的限制包络得到了环面秩的若干重要性质.作为应用,计算了典型李超代数slm|n与限制Cartan型李超代数W(m,n,1),S(m,n,1)的绝对环面秩及S(m,n,1)在W(m,n,1)中的环面秩.
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| 关 键 词： | 限制李超代数 限制包络 环面秩 |
Toral Ranks of Restricted Lie Superalgebras |
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| Li Ping SUN,Wen De LIU.Toral Ranks of Restricted Lie Superalgebras[J].Acta Mathematica Sinica,2021,64(1):167-176. |
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| Authors: | Li Ping SUN Wen De LIU |
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| Institution: | 1.College of Science, Harbin University of Science and Technology, Harbin 150080, P. R. China;2.School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, P. R. China |
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| Abstract: | In this paper, the definitions and properties of torus and toral rank are generalized from modular Lie algebras to super-case. Taking advantage of the restricted envelopes, we obtain certain important results concerning toral rank of modular Lie superalgebras. As an application, the absolute toral ranks of the classical linear Lie superalgebra slm|n, the finite-dimensional restricted Lie superalgebras W(m,n,1) and S(m,n,1) of Cartan type and the toral rank of S(m,n,1) in W(m,n,1) are computed. |
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| Keywords: | restricted Lie superalgebra restricted envelope toral rank |
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