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

Abstract

Let $L$ be a Lie algebra over arbitrary field $k$ with dim $L$ =3 and dim $L^{\prime }$ =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.

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• Extending structures for Lie bialgebras