| 一般线性李超代数在广义Witt李超代数中的中心化子 |
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| 引用本文： | 茅丹,郑克礼. 一般线性李超代数在广义Witt李超代数中的中心化子[J]. 吉林大学学报(理学版), 2022, 60(1): 27-0034. DOI: 10.13413/j.cnki.jdxblxb.2021120 |
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| 作者姓名： | 茅丹 郑克礼 |
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| 作者单位： | 东北林业大学 理学院, 哈尔滨 150040 |
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| 摘 要： | 利用同调方法讨论一般线性李超代数的一类中心化子. 首先将一般线性李超代数分为gl(m,n),gl(m,0),gl(0,n)三种情形进行结构分析, 其中m,n均不为0; 然后分别计算这三种情形在广义Witt李超代数偶部和奇部中的中心化子; 最后给出该类中心化子的结构.
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| 关 键 词： | 中心化子 李超代数 零维上同调群 |
| 收稿时间： | 2021-03-25 |
Centralizer of General Linear Lie Superalgebra in Generalized Witt Lie Superalgebra |
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| MAO Dan,ZHENG Keli. Centralizer of General Linear Lie Superalgebra in Generalized Witt Lie Superalgebra[J]. Journal of Jilin University: Sci Ed, 2022, 60(1): 27-0034. DOI: 10.13413/j.cnki.jdxblxb.2021120 |
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| Authors: | MAO Dan ZHENG Keli |
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| Affiliation: | College of Science, Northeast Forestry University, Harbin 150040, China |
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| Abstract: | We discussed a class of centralizer of the general linear Lie superalgebra by using homological method. Firstly, the general linear Lie superalgebras were divided into three cases for structural analysis, namely, gl(m,n),gl(m,0) and gl(0,n), where m and n were not zero. Secondly, the centralizers of the even and odd situation of the three cases in the generalized Witt Lie superalgebras were calculated respectively. Finally, the structure of this kind of centralizer was given. |
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| Keywords: | centralizer Lie superalgebra zero cohomology group |
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