| 白瑞蒲,吴婴丽.具有β(L)=m-3的m-维非交换3-李代数的分类*[J].数学年刊A辑,2021,42(3):259~268 |
| 具有β(L)=m-3的m-维非交换3-李代数的分类* |
| The Classification of m-Dim Noncommutative 3-Lie Algebras with β(L) = m − 3 |
| Received:February 25, 2020 Revised:December 12, 2020 |
| DOI：10.16205/j.cnki.cama.2021.0020 |
| 中文关键词: 3-李代数, 导代数, 中心 |
| 英文关键词:3-Lie algebra, Derivation algebra, Center |
| 基金项目:河北省自然科学基金(No.20182011126) |
| Author Name | Affiliation | | BAI Ruipu | College of Mathematics and Information Science, Hebei University, Baoding 071002, Hebei, China
Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province, Baoding 071002, Hebei, China. | | WU Yingli | College of Mathematics and Information Science, Hebei University, Baoding 071002, Hebei, China
Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province, Baoding 071002, Hebei, China. |
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| 中文摘要: |
| 对特征零域F上具有β(L)=m-3的m-维非交换3-李代数的结构进行了分类, 且给出了每一类3-李代数的具体乘法结构.证明了满足β(L)=m-3且中心含在导代数的非交换3-李代数的维数小于等于11,大于等于5, 且导代数维数等于1时的3-李代数仅有两类, 导代数维数等于2 时有24类. |
| 英文摘要: |
| m-Dimensional noncommutative 3-Lie algebras with β(L) = m- 3 over a field of characteristic zero are classified, and the exact multiplications are provided. It is proved that if the center of L is contained in L1, then 5 6 m 6 11. And in the cases dim L1 = 1 and 2, there exist only 2 classes and 24 classes non-isomorphic 3-Lie algebras, respectively. |
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