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| 摘要: |
| Filiform李代数作为一类特殊的幂零李代数, 在代数的分类上具有重要作用, 本文研究了一类特殊的可解李代数, 此类李代数是一类具有自然阶化Filiform 幂零根基{n}_{n,1}的可解李代数. 李代数的结构是李代数的重要研究方向之一, 而Hom- 结构对于李代数结构理论的研究具有重要意义. 在特征零代数闭域F 上, 本文计算了此类可解李代数的Hom-结构, 并且得到了这些Hom-结构的基底. |
| 关键词: 可解李代数 Hom- 结构 Filiform 幂零根基 |
| DOI： |
| 分类号:O152.5 |
| 基金项目:国家自然科学基金（12271085）；黑龙江省自然科学基金（LH2022A019）；黑龙江省省属高等学校基本科研业务费（2020-KYYWF-1018）；黑龙江大学杰出青年科学基金（JCL202103） |
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| Hom-structures on a class of solvable Lie algebras with filiform nilradical |
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zhangjushuang,yuanjixia
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| Abstract: |
| Filiform Lie algebras, as a special nilpotent Lie algebras, play an important role in the classification of algebras. In this paper, we study a special class of solvable Lie algebras with naturally graded filiform nilradical {n}_{n,1}. The structures of Lie algebras are one of the important research directions of Lie algebras, and the Hom-structures are of great significance for the study of Lie algebra structure theory. In this paper, we calculate the Hom-structures of these solvable Lie algebras over an algebraically closed field F of zero characteristic, and get the bases of these Hom-structures. |
| Key words: solvable Lie algebras Hom-structures filiform nilradical |
