Rota-Baxter operators on $\mathrm{Cur}({\mathrm{sl}}_2(\mathbb{C}))$

Abstract

We classify all Rota-Baxter operators on the simple conformal Lie algebra $\mathrm{Cur}({\mathrm{sl}}_2(\mathbb{C}))$ and clarify which of them arise from the solutions to the conformal classical Yang-Baxter equation due to the connection discovered by Y. Hong and C. Bai in 2020.

arXiv comment21 p

References in corpus (8)

• Splitting of operations, Manin products and Rota-Baxter operators
• Theory of Finite Pseudoalgebras
• On embedding of dendriform algebras into Rota---Baxter algebras
• Simple finite-dimensional double algebras
• Rota-Baxter Operators on Quadratic Algebras
• Conformal classical Yang-Baxter equation, $S$-equation and $\mathcal{O}$-operators
• Homogeneous conformal averaging operators on semisimple Lie algebras
• Conformal $r$-matrix-Nijenhuis structures, symplectic-Nijenhuis structures and $\mathcal{O}N$-structures