Hom-coalgebra cleft extensions and braided tensor Hom-categories of Hom-entwining structures

Authors : Chen QUANGUO, Wang DİNGGUO

Pages : 186-199

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Publication Date : 2019-02-01

Article Type : Research Paper

Abstract :We investigate how the category of Hom-entwined modules can be made into a monoidal category. The sufficient and necessary conditions making the category of Hom-entwined modules have a braiding are given. Also, we formulate the concept of Hom-cleft extension for a Hom-entwining structure, and prove that if $insert ignore into journalissuearticles values(A, \alpha);$ is a $insert ignore into journalissuearticles values(C,\gamma);$-cleft extension, then there is an isomorphism of Hom-algebras between $insert ignore into journalissuearticles values(A, \alpha);$ and  a crossed product Hom-algebra of $A^{coC}$ and $C$.
Keywords : Hom Hopf algebra, Hom entwining structure, cleft extension