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Volume 28, Issue 4
A Maschke Type Theorem for Doi-Hopf $π$-Modules

Quanguo Chen & Jiangang Tang

Commun. Math. Res., 28 (2012), pp. 289-299.

Published online: 2021-05

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  • Abstract

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 $\mathop ⊕ \limits_{α∈π} C_α ⊗ A$ is a generator in the category $^{π-C} U(H)A$.

  • Keywords

integral, Hopf $π$-coalgebra, Hopf algebra, Maschke type theorem.

  • AMS Subject Headings

16W30, 16W50

  • Copyright

COPYRIGHT: © Global Science Press

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  • BibTex
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@Article{CMR-28-289, author = {Chen , Quanguo and Tang , Jiangang}, title = {A Maschke Type Theorem for Doi-Hopf $π$-Modules}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {28}, number = {4}, pages = {289--299}, abstract = {

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 $\mathop ⊕ \limits_{α∈π} C_α ⊗ A$ is a generator in the category $^{π-C} U(H)A$.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19032.html} }
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 -

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 $\mathop ⊕ \limits_{α∈π} C_α ⊗ A$ is a generator in the category $^{π-C} U(H)A$.

Chen , Quanguo and Tang , Jiangang. (2021). A Maschke Type Theorem for Doi-Hopf $π$-Modules. Communications in Mathematical Research . 28 (4). 289-299. doi:
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