Classical Yang-Baxter Equation and Low Dimensional Triangular Lie Bialgebras

Abstract

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 $(L,[\; ],{\Delta }_r,r)$ 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 $dimL\le 3$.

17pages

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