Twisting Hopf algebras from cocycle deformations

TL;DR

This paper explores how cocycle deformations of certain Hopf algebra liftings induce twists in their duals, providing explicit examples and a comprehensive survey of twists in braided categories.

Contribution

It introduces a method to derive twists from cocycle deformations and extends existing techniques with explicit examples and a detailed survey.

Findings

Explicit construction of twists from cocycle deformations

Extension of known twist-defining techniques

Comprehensive survey of twists in braided categories

Abstract

Let $H$ be a Hopf algebra. Any finite-dimensional lifting of $V\in {}^{H}_{H}\mathcal{YD}$ arising as a cocycle deformation of $A=\mathfrak{B}(V)\#H$ defines a twist in the Hopf algebra $A^*$, via dualization. We follow this recipe to write down explicit examples and show that it extends known techniques for defining twists. We also contribute with a detailed survey about twists in braided categories.