A Maschke type theorem for relative Hom-Hopf modules

Guo, Shuangjian, and Chen, Xiu-Li. "A Maschke type theorem for relative Hom-Hopf modules." Czechoslovak Mathematical Journal 64.3 (2014): 783-799. <http://eudml.org/doc/262145>.

@article{Guo2014,
abstract = {Let $(H,\alpha )$ be a monoidal Hom-Hopf algebra and $(A,\beta )$ a right $(H,\alpha )$-Hom-comodule algebra. We first introduce the notion of a relative Hom-Hopf module and prove that the functor $F $ from the category of relative Hom-Hopf modules to the category of right $(A, \beta )$-Hom-modules has a right adjoint. Furthermore, we prove a Maschke type theorem for the category of relative Hom-Hopf modules. In fact, we give necessary and sufficient conditions for the functor that forgets the $(H, \alpha )$-coaction to be separable. This leads to a generalized notion of integrals.},
author = {Guo, Shuangjian, Chen, Xiu-Li},
journal = {Czechoslovak Mathematical Journal},
keywords = {monoidal Hom-Hopf algebra; separable functors; Maschke type theorem; total integral; relative Hom-Hopf module; monoidal Hom-Hopf algebras; separable functors; Maschke type theorems; total integrals; relative Hom-Hopf modules; monoidal categories; splitting sequences},
language = {eng},
number = {3},
pages = {783-799},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A Maschke type theorem for relative Hom-Hopf modules},
url = {http://eudml.org/doc/262145},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Guo, Shuangjian
AU - Chen, Xiu-Li
TI - A Maschke type theorem for relative Hom-Hopf modules
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 3
SP - 783
EP - 799
AB - Let $(H,\alpha )$ be a monoidal Hom-Hopf algebra and $(A,\beta )$ a right $(H,\alpha )$-Hom-comodule algebra. We first introduce the notion of a relative Hom-Hopf module and prove that the functor $F $ from the category of relative Hom-Hopf modules to the category of right $(A, \beta )$-Hom-modules has a right adjoint. Furthermore, we prove a Maschke type theorem for the category of relative Hom-Hopf modules. In fact, we give necessary and sufficient conditions for the functor that forgets the $(H, \alpha )$-coaction to be separable. This leads to a generalized notion of integrals.
LA - eng
KW - monoidal Hom-Hopf algebra; separable functors; Maschke type theorem; total integral; relative Hom-Hopf module; monoidal Hom-Hopf algebras; separable functors; Maschke type theorems; total integrals; relative Hom-Hopf modules; monoidal categories; splitting sequences
UR - http://eudml.org/doc/262145
ER -