# 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…

## 3 Citations

### A cogroupoid associated to preregular forms

- Mathematics
- 2021

We construct a cogroupoid given by preregular forms. This yields a Morita-Takeuchi equivalence between Manin’s universal quantum groups associated to superpotential algebras.

### A Primer on Twists in the Noncommutative Realm focusing on Algebra, Representation Theory, and Geometry

- Mathematics
- 2022

. We review several techniques that twist an algebra’s multiplica- tive structure. We ﬁrst consider twists by an automorphism, also known as Zhang twists, and we relate them to 2-cocycle twists of…

### Twisting Manin's universal quantum groups and comodule algebras

- Mathematics
- 2022

. Let H be a Hopf algebra and σ be a 2-cocycle on H . Using the tensor equivalence between the comodule categories of H and of its 2-cocycle twist H σ , we study twists of superpotentials, comodule…

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