Title: Double Lie algebras and the R-matrix method
Abstract: The R-matrix method plays a central role in the theory of classical integrable systems and naturally leads to a generalization of the classical Yang–Baxter equation, a fundamental condition also appearing in the theory of quantum groups. A key tool in the study of solutions to the classical Yang–Baxter equation is the double Lie algebra constructed from the corresponding Lie bialgebra. In this talk, I will present a framework for constructing double Lie algebras associated with this generalized classical Yang–Baxter equation and discuss their relevance to classical integrability.