Twisting of graded quantum groups and solutions to the quantum YangBaxter equation
Abstract
Let $H$ be a Hopf algebra that is $\mathbb Z$graded as an algebra. We provide sufficient conditions for a 2cocycle 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 2cocycle 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 YangBaxter equation via the FaddeevReshetikhinTakhtajan construction.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.11585
 Bibcode:
 2021arXiv210911585H
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Quantum Algebra;
 16S37;
 16S80;
 16T05;
 16W50;
 17B37
 EPrint:
 In this version, we have updated references throughout our paper (to appear)