The notion of weak Doi-Hopfπ-datum and weak Doi-Hopfπ-module are given as generalizations of an ordinary weak Doi-Hopf datum and weak Doi-Hopf module introduced in （Boehm, 2000）, also as a generalization of a Doi-...The notion of weak Doi-Hopfπ-datum and weak Doi-Hopfπ-module are given as generalizations of an ordinary weak Doi-Hopf datum and weak Doi-Hopf module introduced in （Boehm, 2000）, also as a generalization of a Doi-Hopfπ-module introduced in （Wang, 2004）. Then we also show that the functor forgetting action or coaction has an adjoint. Furthermore we explain how the notion of weak Doi-Hopfπ-datum is related to weak smash product. This paper presents our preliminary results on weak Doi-Hopf group modules.展开更多
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 applic...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 α∈π Ca A is a generator in the category π-Cu（H）A.展开更多
基金Project supported by the Program for New Century Excellent Talents in University (No. 04-0522), the National Science Foundation of Zhejiang Province of China (No. 102028), and the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China (No. 704004)
文摘The notion of weak Doi-Hopfπ-datum and weak Doi-Hopfπ-module are given as generalizations of an ordinary weak Doi-Hopf datum and weak Doi-Hopf module introduced in （Boehm, 2000）, also as a generalization of a Doi-Hopfπ-module introduced in （Wang, 2004）. Then we also show that the functor forgetting action or coaction has an adjoint. Furthermore we explain how the notion of weak Doi-Hopfπ-datum is related to weak smash product. This paper presents our preliminary results on weak Doi-Hopf group modules.
文摘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 α∈π Ca A is a generator in the category π-Cu（H）A.
