(untitled) (Communications in Mathematical Research, 2020)
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_ad^*g^* and some new structures of left-symmetric algebra induced from g and its Rota-Baxter operators.