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| 摘要: |
| 众所周知 3 维李代数在同构意义下有 6 种. 在文献 [12] 中, 作者详细地计算出 3 维单李代数 $sl(2, \mathbb{C})$ 上的 Rota-Baxter 算子和经典 Yang-Baxter 的解. 本文研究的是导代数的维数是 2 的 3 维李代数 $g$ 上的权为零的 Rota-Baxter 算子, 进一步确定了 $g\ltimes_{ad^{*}}g^{*}$ 上相应的经典 Yang-Baxter 的解以及 $g$ 上的新的左对称代数结构. |
| 关键词: Rota-Baxter 算子, 3 维李代数, 经典Yang-Baxter 方程的解, 左对称代数结构 |
| DOI： |
| 分类号:O152.5 |
| 基金项目:国家自然科学基金项目（11047030），河南省科技发展项目（ 152300410061） |
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| Rota-Baxter operators on 3-dimensional Lie algebras and solutions of the classical Yang-Baxter equation I |
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Wu Linli,王梦平,Cheng Yongsheng
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| Abstract: |
| It is well known that there are six kinds of 3-dimensional Lie algebras up to
isomorphism. In [12], the authors explicitly determine all Rota-Baxter operators
on 3-dimensional simple Lie algebra sl(2,C) and the corresponding solutions of the
classical Yang-Baxter equation. In this paper, our aim is to determine Rota-Baxter
operators on the 3-dimensional Lie algebra whose derived algebra’s dimension is 2.
we explicitly determine Rota-Baxter operators (of weight zero) on the 3-dimensional
Lie algebras g. Furthermore, we give the corresponding solutions of the classical
Yang-Baxter equation in the 6-dimensional Lie algebras and some new
structures of left symmetry algebra of g. |
| Key words: Rota-Baxter operators, 3-dimensional Lie algebras, classical Yang-Baxter equa- tion, left symmetry algebra |
