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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

advances in mathematical physics

Rota-Baxter Operators on 3-Dimensional Lie Algebras and the Classical <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:math>-Matrices

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