Cocycle deformations and Galois objects for semisimple Hopf algebras of dimension p3 and pq2

Let p and q be distinct prime numbers. We study the Galois objects and cocycle deformations of the noncommutative, noncocommutative, semisimple Hopf algebras of odd dimension p(3) and of dimension pq(2). We obtain that the p + 1 non-isomorphic self-dual semisimple Hopf algebras of dimension p(3) classified by Masuoka have no non-trivial cocycle deformations, extending his previous results for the 8-dimensional Kac-Paljutkin Hopf algebra. This is done as a consequence of the classification of categorical Morita equivalence classes among semisimple Hopf algebras of odd dimension p(3), established by the third-named author in an appendix. (C) 2017 Elsevier B.V. All rights reserved.