We prove that commutative algebras in braided tensor categories do not admit faithful Hopf algebra actions unless they come from group actions. We also show that a group action allows us to see the algebra as the regular algebra in the representation category of the acting group.

中文翻译：

---

张量类别中的霍夫代数作用

我们证明了编织张量类别中的可交换代数不接受忠实的Hopf代数运算，除非它们来自组运算。我们还表明，群体行为使我们能够将代数视为行为群体的代表类别中的常规代数。