Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation.

Let be a Hopf algebra that is -graded as an algebra. We provide sufficient conditions for a 2-cocycle twist of to be a Zhang twist of . In particular, we introduce the notion of a twisting pair for such that the Zhang twist of by such a pair is a 2-cocycle twist. We use twisting pairs to describe twists of Manin's universal quantum groups associated with quadratic algebras and provide twisting of solutions to the quantum Yang-Baxter equation via the Faddeev-Reshetikhin-Takhtajan construction.