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

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.

In this version, we have updated references throughout our paper (to appear)

References in corpus (2)

• G-algebras, twistings, and equivalences of graded categories
• The quantum group of a preregular multilinear form