AI 中文总结
本文定义了 Hopf 代数余作用的 Hopf 像为最小可分解子代数，证明其内忠实性，并针对 Nichols 代数给出检测结果及玻色化实例。
AI 中文摘要
我们引入一个 Hopf 代数在代数上的右余作用的 Hopf 像，定义为使该余作用可分解的最小子 Hopf 子代数。我们建立了其基本性质，并证明在 Hopf 像上诱导的余作用是内忠实的。对于由 Yetter–Drinfeld 模产生的 Nichols 代数上的余作用，我们证明了 Hopf 像是由 Yetter–Drinfeld 模上的底层余作用所检测到的最小子 Hopf 子代数。我们给出了由玻色化产生的真非平凡 Hopf 像的显式例子。
英文摘要
We introduce the Hopf image of a right coaction of a Hopf algebra on an algebra as the smallest Hopf subalgebra through which the coaction factors. We establish its basic properties and show that the induced coaction on the Hopf image is inner-faithful. For coactions on Nichols algebras arising from Yetter--Drinfeld modules, we prove that the Hopf image is the smallest Hopf subalgebra detected by the underlying coaction on the Yetter--Drinfeld module. We give explicit examples of proper non-trivial Hopf images arising from bosonizations.
CommentsPreprint, 17 pages, Comments are welcome
