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Two-sided Two-cosided Hopf Modules and Yetter–Drinfeld Modules for Quasi-Hopf Algebras

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Abstract

For a quasi-Hopf algebra H, an H-bicomodule algebra \(\mathbb{A}\) and an H-bimodule coalgebra C we will show that the category of two-sided two-cosided Hopf modules \({}^C_H{\cal M}_{\mathbb{A}}^H\) is equivalent to the category of right–left generalized Yetter–Drinfeld modules \({}^C{\cal YD}(H)_{\mathbb{A}}\). Using alternative versions of this result we will recover the category isomorphism between the categories of left–left and left–right Yetter–Drinfeld modules over a quasi-Hopf algebra.

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Bulacu, D., Torrecillas, B. Two-sided Two-cosided Hopf Modules and Yetter–Drinfeld Modules for Quasi-Hopf Algebras. Appl Categor Struct 14, 503–530 (2006). https://doi.org/10.1007/s10485-006-9045-4

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