Classical Yang- Baxter Equation and Low Dimensional Triangular Lie Bialgebras Over Arbitrary Field

Let $L$ be a Lie algebra over arbitrary field $k$ with dim $L$ =3 and dim $L'$ =2. All solutions of constant classical Yang- Baxter equation (CYBE) in Lie algebra $L$ are obtained and the necessary conditions which $(L,[\ ],\Delta_{r}, r)$ is a coboundary (or triangular) Lie bialgebra are given.