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

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Huang, Hongdi; Nguyen, Van C.; Ure, Charlotte; Vashaw, Kent B.; Veerapen, Padmini; ... Show more
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Abstract
Abstract Let H be a Hopf algebra that is ℤ $\mathbb Z$ -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-Takhtajan construction.
Date issued
2022-12-01
URI
https://hdl.handle.net/1721.1/146745
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Springer US
Citation
Huang, Hongdi, Nguyen, Van C., Ure, Charlotte, Vashaw, Kent B., Veerapen, Padmini et al. 2022. "Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation."
Version: Final published version
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