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Entwined Hom-modules and frobenius properties
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Entwined Hom-modules were introduced by Karacuha in [13], which can be viewed
as a generalization of Doi-Hom Hopf modules and entwined modules. In this
paper, the sufficient and necessary conditions for the forgetful functor F : ?H(Mk)(?)CA ? ?H(Mk)A and its adjoint G : ?H(Mk)A ? ?H (Mk)(?)CA form
a Frobenius pair are obtained, one is that A?C and the C*?A are isomorphic as
(A;C*op#A)-bimodules, where (A,C,?) is a Hom-entwining structure. Then we
can describe the isomorphism by using a generalized type of integral. As an
application, a Maschke type theorem for entwined Hom-modules is given.
Title: Entwined Hom-modules and frobenius properties
Description:
Entwined Hom-modules were introduced by Karacuha in [13], which can be viewed
as a generalization of Doi-Hom Hopf modules and entwined modules.
In this
paper, the sufficient and necessary conditions for the forgetful functor F : ?H(Mk)(?)CA ? ?H(Mk)A and its adjoint G : ?H(Mk)A ? ?H (Mk)(?)CA form
a Frobenius pair are obtained, one is that A?C and the C*?A are isomorphic as
(A;C*op#A)-bimodules, where (A,C,?) is a Hom-entwining structure.
Then we
can describe the isomorphism by using a generalized type of integral.
As an
application, a Maschke type theorem for entwined Hom-modules is given.
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