Categorical Morita equivalence and monoidal Morita equivalence of semisimple Hopf algebras of dimension pqr

Abstract

In this paper, we determine the cocycle deformations and Galois objects for semisimple Hopf algebras of dimension pqr, and decide the categorically Morita equivalent classes and monoidally Morita equivalent classes of them. We show that all of them only have one trivial Galois objects, therefore these Hopf algebras are pairwise twist inequivalent, equivalently they are not monoidally Morita equivalent to each other, moreover, all the categorically Morita equivalent classes are determined.