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

Abstract

In this paper, we describe the Galois objects for semisimple Hopf algebras of dimension [Formula: see text], where [Formula: see text] are distinct primes. We show that each of these Hopf algebras has only one trivial Galois object, so that they are pairwise twist inequivalent; equivalently, they are not monoidally Morita equivalent to each other. Moreover, we determine the categorical and monoidal Morita equivalence classes of these Hopf algebras.