| 无限维齐性Rota-Baxter 3-李代数(Ⅱ) |
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| 引用本文： | 白瑞蒲,刘山.无限维齐性Rota-Baxter 3-李代数(Ⅱ)[J].河北大学学报(自然科学版),2022,42(4):343. |
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| 作者姓名： | 白瑞蒲 刘山 |
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| 基金项目： | 河北省自然科学基金资助项目(20182011126) |
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| 摘 要： | 利用无限维单3-李代数Aω上权为1且满足g(0)+g(1)+1=0的齐性Rota-Baxter算子Rk,构造了13类齐性Rota-Baxter 3-李代数Ak,1≤k≤13,证明了在齐性Rota-Baxter 3-李代数Ak中存在5类两两不同构的齐性Rota-Baxter 3-李代数Di,并研究了每一类3-李代数Di的结构,1≤i≤5.
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| 关 键 词： | 3-李代数 Rota-Baxter算子 齐性Rota-Baxter 3-李代数 |
| 收稿时间： | 2021-02-06 |
Infinite dimensional homogenous Rota-Baxter 3-Lie algebras(Ⅱ) |
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| BAI Ruipu,LIU Shan.Infinite dimensional homogenous Rota-Baxter 3-Lie algebras(Ⅱ)[J].Journal of Hebei University (Natural Science Edition),2022,42(4):343. |
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| Authors: | BAI Ruipu LIU Shan |
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| Institution: | College of Mathematics and Information Science, Hebei University, Baoding 071002, China |
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| Abstract: | 13 classes of homogeneous Rota-Baxter 3-Lie algebras Ak are constructed by using the homogeneous Rota-Baxter operators Rk, 1≤k≤13, with weight 1 and satisfying g(0)+g(1)+1=0 on infinite dimensional simple 3-Lie algebra Aω. It is proved that there are 5 classes of non-isomorphic homogeneous Rota-Baxter 3-Lie algebras Di,1≤i≤5, in the homogeneous Rota-Baxter 3-Lie Algebra Ak,1≤k≤13, and the structure of each class of 3-Lie algebras Di, 1≤i≤5, is studied. |
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| Keywords: | 3-Lie algebra Rota-Baxter operator homogenous Rota-Baxter 3-Lie algebra |
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