Volume 35, Issue 1
Rota-Baxter Operators on 3-Dimensional Lie Algebras and Solutions of the Classical Yang-Baxter Equation

Commun. Math. Res., 35 (2019), pp. 81-96.

Published online: 2019-12

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• Abstract

In this paper, we compute Rota-Baxter operators on the 3-dimensional Lie algebra $g$ whose derived algebra's dimension is 2. Furthermore, we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras $g\ltimes_{ad^*}g^*$ and some new structures of left-symmetric algebra induced from $g$ and its Rota-Baxter operators.

• Keywords

Rota-Baxter operators, 3-dimensional Lie algebra, classical Yang-Baxter equation, left-symmetric algebra

17B10, 17B65, 17B68

yscheng@henu.edu.cn (Yongsheng Cheng)

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@Article{CMR-35-81, author = {Yongsheng and Cheng and yscheng@henu.edu.cn and 5922 and School of Mathematics and Statistics, Henan University, Kaifeng, Henan, 475004 and Yongsheng Cheng and Linli and Wu and and 5923 and School of Mathematics and Statistics, Henan University, Kaifeng, Henan, 475004 and Linli Wu and Panyin and Wang and and 5925 and School of Mathematics and Statistics, Henan University, Kaifeng, Henan, 475004 and Panyin Wang}, title = {Rota-Baxter Operators on 3-Dimensional Lie Algebras and Solutions of the Classical Yang-Baxter Equation}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {35}, number = {1}, pages = {81--96}, abstract = {

In this paper, we compute Rota-Baxter operators on the 3-dimensional Lie algebra $g$ whose derived algebra's dimension is 2. Furthermore, we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras $g\ltimes_{ad^*}g^*$ and some new structures of left-symmetric algebra induced from $g$ and its Rota-Baxter operators.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2019.01.09}, url = {http://global-sci.org/intro/article_detail/cmr/13477.html} }
TY - JOUR T1 - Rota-Baxter Operators on 3-Dimensional Lie Algebras and Solutions of the Classical Yang-Baxter Equation AU - Cheng , Yongsheng AU - Wu , Linli AU - Wang , Panyin JO - Communications in Mathematical Research VL - 1 SP - 81 EP - 96 PY - 2019 DA - 2019/12 SN - 35 DO - http://doi.org/10.13447/j.1674-5647.2019.01.09 UR - https://global-sci.org/intro/article_detail/cmr/13477.html KW - Rota-Baxter operators, 3-dimensional Lie algebra, classical Yang-Baxter equation, left-symmetric algebra AB -

In this paper, we compute Rota-Baxter operators on the 3-dimensional Lie algebra $g$ whose derived algebra's dimension is 2. Furthermore, we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras $g\ltimes_{ad^*}g^*$ and some new structures of left-symmetric algebra induced from $g$ and its Rota-Baxter operators.

Yongsheng Cheng, Linli Wu & Panyin Wang. (2019). Rota-Baxter Operators on 3-Dimensional Lie Algebras and Solutions of the Classical Yang-Baxter Equation. Communications in Mathematical Research . 35 (1). 81-96. doi:10.13447/j.1674-5647.2019.01.09
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