| 与一类unit型相联系的有限维单李代数的结构 |
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| 引用本文： | 于亚龙,陈正新.与一类unit型相联系的有限维单李代数的结构[J].数学研究及应用,2019,39(5):469-488. |
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| 作者姓名： | 于亚龙 陈正新 |
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| 作者单位： | 福建师范大学数学与信息学院, 福建 福州 350117,福建师范大学数学与信息学院, 福建 福州 350117 |
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| 基金项目： | 国家自然科学基金(Grant No.11571360),福建省自然科学基金(Grant Nos.2016J01006; JZ160427). |
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| 摘 要： | Let n ≥ 4. The complex Lie algebra, which is attached to the unit form q(x1, x2,..., xn)■ and defined by generators and generalized Serre relations, is proved to be a finite-dimensional simple Lie algebra of type Dn, and realized by the Ringel-Hall Lie algebra of a Nakayama algebra. As its application of the realization, we give the roots and a Chevalley basis of the simple Lie algebra.
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| 关 键 词： | Nakayama 代数 有限维单李代数 Ringel-Hall 李代数. |
| 收稿时间： | 2017/11/4 0:00:00 |
| 修稿时间： | 2018/9/1 0:00:00 |
The Structure of a Lie Algebra Attached to a Unit Form |
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| Yalong YU and Zhengxin CHEN.The Structure of a Lie Algebra Attached to a Unit Form[J].Journal of Mathematical Research with Applications,2019,39(5):469-488. |
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| Authors: | Yalong YU and Zhengxin CHEN |
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| Abstract: | Let $n\geq 4$. The complex Lie algebra, which is attached to the unit form $\mathfrak{q}(x_1,x_2,\ldots, x_n)=\sum_{i=1}^nx_i^2-(\sum_{i=1}^{n-1}x_ix_{i+1})+x_1x_n $ and defined by generators and generalized Serre relations, is proved to be a finite-dimensional simple Lie algebra of type $\mathbb{D}_n$, and realized by the Ringel-Hall Lie algebra of a Nakayama algebra. As its application of the realization, we give the roots and a Chevalley basis of the simple Lie algebra. |
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| Keywords: | Nakayama algebras finite dimensional simple Lie algebras Ringel-Hall Lie algebras |
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