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 $C$.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:We investigate how the category of Hom-entwined modules can be made into a monoidal category.
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Temel Bulgular & Veri:The sufficient and necessary conditions making the category of Hom-entwined modules have a braiding are given.
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Sonuç & Katkı: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 $C$.
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 $C$.
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