| 具有导子的李三系的中心扩张与形变 |
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| 引用本文： | 郭双建.具有导子的李三系的中心扩张与形变[J].数学研究及应用,2022,42(2):189-198. |
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| 作者姓名： | 郭双建 |
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| 作者单位： | 贵州财经大学数学与统计学院, 贵州 贵阳 550025 |
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| 基金项目： | 国家自然科学基金(Grant No.12161013),贵州省科技厅基金(Grant No.[2020]1Y005). |
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| 摘 要： | 考虑具有导子的李三系.由李三系和一个导子称为LietsDer对.定义系数在表示中的LietsDer对的上同调理论.研究LietsDer对的中心扩张.接下来,将形变理论推广到由李三系和导子构成LietsDer对上,它由带有系数的LietsDer对的上同调所支配.
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| 关 键 词： | 李三系 导子 表示 上同调 中心扩张 形变 |
| 收稿时间： | 2020/12/29 0:00:00 |
| 修稿时间： | 2021/4/28 0:00:00 |
Central Extensions and Deformations of Lie Triple Systems with a Derivation |
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| Shuangjian GUO.Central Extensions and Deformations of Lie Triple Systems with a Derivation[J].Journal of Mathematical Research with Applications,2022,42(2):189-198. |
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| Authors: | Shuangjian GUO |
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| Institution: | School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guizhou 550025, P. R. China |
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| Abstract: | In this paper, we consider Lie triple systems with derivations. A pair consisting of a Lie triple system and a distinguished derivation is called a LietsDer pair. We define a cohomology theory for LietsDer pair with coefficients in a representation. We study central extensions of a LietsDer pair. In the next, we generalize the formal deformation theory to LietsDer pairs in which we deform both the Lie triple system bracket and the distinguished derivation. It is governed by the cohomology of LietsDer pair with coefficients in itself. |
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| Keywords: | Lie triple system derivation representation cohomology central extension deformation |
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