Twisting Hopf algebras from cocycle deformations

Abstract

Let H be a Hopf algebra. Any finite-dimensional lifting of V∈HHYD arising as a cocycle deformation of A= 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.