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

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

2006-03-30

arxiv.org/abs/math/0603697v2

International Mathematical Journal, 2 (2002) 8, 825-831

Mathematics

Rings and Algebras

7pages

Scientific paper

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.

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