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Constructing braided Hopf algebras in monoidal Hom-category. (English) Zbl 1357.16051

Summary: In this paper, we first define the coquasitriangular monoidal Hom-Hopf algebras. Secondly, we present a method to construct braided monoidal Hom-Hopf algebras \(\overline{B}\) and \(\underline{B}\) in Yetter-Drinfeld category \(\widetilde{\mathcal{H}}(_{H}\mathcal{YD}_1^{H})\) and \(\widetilde{\mathcal{H}}(_{H}\mathcal{YD}_2^{H})\) respectively. As applications, we study some special cases in both module and comodule form for \((H, \xi_H)\) being quasitriangular and for \((H, \xi_H)\) being coquasitriangular respectively. Finally, we give some applications and examples of braided monoidal Hom-Hopf algebras in this article.

MSC:

16T05 Hopf algebras and their applications
18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
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