Yetter–Drinfeld modules under cocycle twists

We give an explicit formula for the correspondence between simple Yetter–Drinfeld modules for certain finite-dimensional pointed Hopf algebras H and those for cocycle twists Hσ of H. This implies an equivalence between modules for their Drinfeld doubles. To illustrate our results, we consider the restricted two-parameter quantum groups ur,s(sln) under conditions on the parameters guaranteeing that ur,s(sln) is a Drinfeld double of its Borel subalgebra. We determine explicit correspondences between ur,s(sln)-modules for different values of r and s and provide examples where no such correspondence can exist. Our examples were obtained via the computer algebra system Singular::Plural.