Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation
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31_2022_Article_9779.pdf
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1.25 MB
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Author(s)
Huang, Hongdi
Nguyen, Van C.
Ure, Charlotte
Vashaw, Kent B.
Veerapen, Padmini
Wang, Xingting
Date Issued
December 1, 2022
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00031-022-09779-9
