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arXiv · 2109.11585

Twisting of graded quantum groups and solutions to the quantum Yang-Baxter equation

Hongdi Huang·Van C. Nguyen·Charlotte Ure·Kent B. Vashaw·Padmini Veerapen·Xingting Wang
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Abstract

Let $H$ be a Hopf algebra that is $\mathbb Z$-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 to quadratic algebras and provide twisting of solutions to the quantum Yang-Baxter equation via the Faddeev-Reshetikhin-Takhtajan construction.

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Hongdi Huang, Van C. Nguyen, Charlotte Ure, Kent B. Vashaw, Padmini Veerapen, Xingting Wang. 2021-09-23. Twisting of graded quantum groups and solutions to the quantum Yang-Baxter equation. https://arxiv.org/abs/2109.11585

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