Rota-Baxter Operators on 3-Dimensional Lie Algebras and the Classical R-Matrices

Abstract EN

Our aim is to classify the Rota-Baxter operators of weight 0 on the 3-dimensional Lie algebra whose derived algebra’s dimension is 2.

We explicitly determine all Rota-Baxter operators (of weight zero) on the 3-dimensional Lie algebras g.

Furthermore, we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ⋉ad⁎ g⁎ and the induced left-symmetry algebra structures on g.