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 - <p style="text-align: justify;">In this paper, we compute Rota-Baxter operators on the 3-dimensional Lie algebra $g$ whose derived algebra&#39;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.</p>