Rota-Baxter Operators on 3-Dimensional Lie Algebras and Solutions of the Classical Yang-Baxter Equation

Authors

  • Yongsheng Cheng School of Mathematics and Statistics, Henan University, Kaifeng, Henan, 475004
  • Linli Wu School of Mathematics and Statistics, Henan University, Kaifeng, Henan, 475004
  • Panyin Wang School of Mathematics and Statistics, Henan University, Kaifeng, Henan, 475004

DOI:

https://doi.org/10.13447/j.1674-5647.2019.01.09

Keywords:

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

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.

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Published

2020-03-18

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Issue

Vol. 35 No. 1 (2019)

Section

Articles

How to Cite

Rota-Baxter Operators on 3-Dimensional Lie Algebras and Solutions of the Classical Yang-Baxter Equation. (2020). Communications in Mathematical Research, 35(1), 81-96. https://doi.org/10.13447/j.1674-5647.2019.01.09