Dynamical Twists in Hopf Algebras

Abstract

We establish a bijective correspondence between gauge equi- valence classes of dynamical twists in a finite-dimensional Hopf algebra H based on a finite abelian group A and equivalence classes of pairs (K,{V�} �∈ b A ), where K is an H-simple left H-comodule semisimple al- gebra and {V�}�∈ b A is a family of irreducible representations satisfy- ing certain conditions. Our results generalize the results obtained by Etingof-Nikshych on the classification of dynamical twists in group al- gebras.