Entwined Hom-modules and frobenius properties | Zendy

Shuangjian Guo | Zendy; Xiaohui Zhang | Zendy; Yuanyuan Ke | Zendy

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Entwined Hom-modules and frobenius properties

Author(s) -

Shuangjian Guo,

Xiaohui Zhang,

Yuanyuan Ke

Publication year - 2019

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1911307g

Subject(s) - mathematics , functor , isomorphism (crystallography) , generalization , type (biology) , pure mathematics , algebra over a field , mathematical analysis , crystallography , chemistry , crystal structure , ecology , biology

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 : H̃ (Mk)(ψ)A → H̃ (Mk)A and its adjoint G : H̃ (Mk)A → H̃ (Mk)(ψ)A 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, ψ) 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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