TY - JOUR
T1 - A Maschke Type Theorem for Doi-Hopf $π$-Modules
AU - Chen , Quanguo
AU - Tang , Jiangang
JO - Communications in Mathematical Research 
VL - 4
SP - 289
EP - 299
PY - 2021
DA - 2021/05
SN - 28
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19032.html
KW - integral, Hopf $π$-coalgebra, Hopf algebra, Maschke type theorem.
AB - <p style="text-align: justify;">We prove a Maschke type theorem for Doi-Hopf $π$-modules. A sufficient
condition for having a Maschke type property is that there exists a suitable total
integral map for the Doi-Hopf $π$-modules in question. The applications of the results
are considered. Finally, As an application of the existence of total integral, we prove
that $\mathop&nbsp;⊕ \limits_{α∈π} C_α ⊗ A$ is a generator in the category $^{π-C} U(H)A$.</p>