Integration and geometrization of Rota-Baxter Lie algebras
Integration and geometrization of Rota-Baxter Lie algebras
复制标题
Rota-Baxter 李代数的积分和几何化
DOI：
10.1016/j.aim.2021.107834
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发表时间：
2020-09
影响因子：
1.7
通讯作者：
Yunhe Sheng
中科院分区：
文献类型：
--
作者：
Li Guo;Honglei Lang;Yunhe Sheng
作为经典的Yang-Baxter方程的算子形式，Belavin，Drinfeld和Semenov-Tian-Shansky首先研究了李代数上的Rota-Baxter算子。作为研究可积系统的基本工具，Semenov-Tian-Shansky通过从修正的Yang-Baxter方程的解积分李代数的因式分解，得到了李群的因式分解定理。结合李代数上的Rota-Baxter算子，我们引入了李群和更一般的群上的Rota-Baxter算子的概念。这样，分解定理就可以直接在群上实现。在几何化方面，引入了Rota-Baxter李代数体和Rota-Baxter李群胚的概念。Rota-Baxter李代数体自然产生后李代数体。此外，Rota-Baxter李代数或Rota-Baxter李群的几何化可以通过它在流形上的作用来实现。给出了这些新概念的实例和应用。
Rota-Baxter operators on Lie algebras were first studied by Belavin, Drinfeld and Semenov-Tian-Shansky as operator forms of the classical Yang-Baxter equation. As a fundamental tool in studying integrable systems, the factorization theorem of Lie groups by Semenov-Tian-Shansky was obtained by integrating a factorization of Lie algebras from solutions of the modified Yang-Baxter equation. Integrating the Rota-Baxter operators on Lie algebras, we introduce the notion of Rota-Baxter operators on Lie groups and more generally on groups. Then the factorization theorem can be achieved directly on groups. For geometrization, the notions of Rota-Baxter Lie algebroids and Rota-Baxter Lie groupoids are introduced. A Rota-Baxter Lie algebroid naturally gives rise to a post-Lie algebroid. Furthermore, the geometrization of a Rota-Baxter Lie algebra or a Rota-Baxter Lie group can be realized by its action on a manifold. Examples and applications are provided for these new notions.
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左对称代数体
影响因子：
1
作者：
Jiefeng Liu;Yunhe Sheng;Chengming Bai;Zhiqi Chen
通讯作者：
Zhiqi Chen
DOI：
10.1090/s0002-9904-1969-12156-7
发表时间：
1969-03
影响因子：
1.3
作者：
G. Rota
通讯作者：
G. Rota
影响因子：
3
作者：
BAXTER, RJ
通讯作者：
BAXTER, RJ
影响因子：
8.6
作者：
C. Yang
通讯作者：
C. Yang
DOI：
10.1007/978-3-0348-8003-9_4
发表时间：
2002-09
期刊：
arXiv: Exactly Solvable and Integrable Systems
影响因子：
--
作者：
M. Semenov-Tian-Shansky
通讯作者：
M. Semenov-Tian-Shansky