Cocycle deformations and Galois objects of semisimple Hopf algebras of dimension 16

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.

Keywords:

• Cocycle deformations
• Frobenius-Schur indicators
• Galois objects
• semisimple Hopf algebras

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16T05
• 16S35
• 18D10

Acknowledgments

The authors would like to appreciate the continued encouragement and help from their PhD supervisor Prof. Naihong Hu. This article started after reading [2], we are grateful to the authors in [2], 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.

Additional information

Funding

The authors were partially supported by the NSFC (Grant Nos. 11771142 and 11926353).