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

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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… Click to show full 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 $(A, \alpha)$ is a $(C,\gamma)$-cleft extension, then there is an isomorphism of Hom-algebras between $(A, \alpha)$ and  a crossed product Hom-algebra of $A^{coC}$ and $C$.

Keywords: hom; hom entwining; cleft; hom coalgebra; cleft extensions; coalgebra cleft

Journal Title: Hacettepe Journal of Mathematics and Statistics
Year Published: 2017

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