Classical Yang-Baxter Equation and Low Dimensional Triangular Lie Bialgebras

All solutions of constant classical Yang-Baxter equation (CYBE) in Lie algebra $L$ with dim $L\le 3$ are obtained and the sufficient and necessary conditions which $(L,\text{[ ]},{\mathrm{\Delta }}_r,r)$ is a coboundary (or triangular) Lie bialgebra are given. The strongly symmetric elements in $L\otimes L$ are found and they all are solutions of CYBE in $L$ with $dim L \le 3$.