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.

22 pages

References in corpus (2)

• Central Invariants and Frobenius-Schur Indicators for Semisimple Quasi-Hopf Algebras
• On the Equivalence of Module Categories over a Group-Theoretical Fusion Category

Cited by in corpus (1)

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