Rota-Baxter operators on 3-dimensional Lie algebras and the classical \(R\)-matrices
Summary: 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 \(g \ltimes_{\mathrm{ad}^\ast} g^\ast\) and the induced left-symmetry algebra structures on \(g\).
scientific article; zbMATH DE number 6962647
scientific article