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

@article{Huang2022TwistingOG,
  title={Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation},
  author={Hongdi Huang and Van C. Nguyen and Charlotte Ure and Kent B. Vashaw and Padmini Veerapen and Xingting Wang},
  journal={Transformation Groups},
  year={2022}
}
Let H be a Hopf algebra that is $\mathbb Z$ ℤ -graded as an algebra. We provide sufficient conditions for a 2-cocycle twist of H to be a Zhang twist of H. In particular, we introduce the notion of a twisting pair for H such that the Zhang twist of H 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… 

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