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Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation
Hongdi Huang1, Van C Nguyen2, Charlotte Ure3
1Department of Mathematics, Rice University, Houston, TX 77005 USA.
Abstract:
Let H be a Hopf algebra that is -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.
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