| Filiform李代数Q_n的Hom-结构 |
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| 引用本文： | 于欢欢,刘文德. Filiform李代数Q_n的Hom-结构[J]. 纯粹数学与应用数学, 2015, 0(2): 156-163. DOI: 10.3969/j.issn.1008-5513.2015.02.006 |
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| 作者姓名： | 于欢欢 刘文德 |
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| 作者单位： | 哈尔滨师范大学数学科学学院,黑龙江 哈尔滨,150025 |
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| 基金项目： | 国家自然科学基金，黑龙江省杰出青年基金 |
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| 摘 要： | 首先证明了有限维Z-阶化李代数上的一个线性算子是Hom-结构的充分必要条件,即它的每个齐次分支也是Hom-结构.然后计算了特征零代数闭域上一类有限维Z-阶化Filiform李代数Qn的齐次Hom-结构,从而决定了Qn的所有Hom-结构.
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| 关 键 词： | Filiform李代数 阶化结构 Hom-结构 |
The Hom-structures on Filiform Lie algebras Qn |
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| Yu Huanhuan,Liu Wende. The Hom-structures on Filiform Lie algebras Qn[J]. Pure and Applied Mathematics, 2015, 0(2): 156-163. DOI: 10.3969/j.issn.1008-5513.2015.02.006 |
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| Authors: | Yu Huanhuan Liu Wende |
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| Affiliation: | Yu Huanhuan;Liu Wende;Department of Mathematics, Harbin Normal University; |
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| Abstract: | In this paper, we prove that a linear operator on a finite-dimensional Z-graded Lie algebra is a Hom-structure if and only if its homogeneous components are Hom-structures. We also compute homogeneous Hom-structures on a finite dimensional Z-graded Filiform Lie algebra Qn over an algebraically closed field of characteristic zero. As a consequence, we determine all the Hom-structures on Qn. |
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| Keywords: | Filiform Lie algebra graded structure Hom-structure |
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