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.

中文翻译：

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16 维半简单 Hopf 代数的 Cocycle 变形和 Galois 对象

摘要 在本文中，我们确定了维数为 16 的非交换和非交换半单 Hopf 代数的共循环变形和伽罗瓦对象。三个 Hopf 代数是对偶群代数的共轮变形，它们都不允许非平凡的共轮变形。