AbstractRota-Baxter operators on Lie algebras were first studied by Belavin, Drinfeld and Semenov-Tian-Shansky as operator forms of the classical Yang-Baxter equation. As a fundamental tool in studying integrable systems, the factorization theorem of Lie groups by Semenov-Tian-Shansky was obtained by integrating a factorization of Lie algebras from solutions of the modified Yang-Baxter equation...
Abstract:In the first part of this talk, I will briefly introduce categorification of acyclic quantum cluster algebras by cluster categories of acyclic quivers, based on the work of Fan Qin. In the second part, I will explain how to categorify certain quantum cluster algebras using cluster categories of coherent sheaves on weighted projective lines. Concretely, we firstly define specialized qu...