Abstract
In this article, we determine cocycle deformations and Galois objects of non-commutative and non-cocommutative semisimple Hopf algebras of dimension 16. We show that these Hopf algebras are pairwise twist inequivalent mainly by calculating their higher Frobenius-Schur indicators, and that except three Hopf algebras which are cocycle deformations of dual group algebras, none of them admit non-trivial cocycle deformations.
Acknowledgments
The authors would like to appreciate the continued encouragement and help from their PhD supervisor Prof. Naihong Hu. This article started after reading [Citation2], we are grateful to the authors in [Citation2], specially thanks to Prof. Chelsea Walton for her valuable suggestions and comments on earlier version of the manuscript. The authors thanks the referees for numerous suggestions on improving this paper.