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.