群缠绕模范畴的可分函子

Separable Functors of the Category for Group-entwined Modules

设π是1个群.在Hopfπ-代数情形下,π-缠绕结构和π-缠绕模的概念被引入,并得到了π-缠绕模范畴上的忘却函子可分的充要条件,其中忘却函子忘却的是π-模作用.最后,作为应用证明了π-缠绕模的Maschke-type定理.

Let n be a group. In this note, we introduce the definition of π-entwining structures and n-entwined modules over Hopf π-algebras, and obtain necessary and sufficient conditions for the functor on the category of π-entwined modules that forgets the π-A-action to he separable. As an application, we prove the Maschke-type theorem for n-entwined modules.