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Invertible bimodule categories over the representation category of a Hopf algebra. (English) Zbl 1305.18020
Summary: For any finite-dimensional Hopf algebra \(H\) we construct a group homomorphism \(\text{BiGal}(H) \to \text{BrPic}(\text{Rep}(H))\), from the group of equivalence classes of \(H\)-biGalois objects to the group of equivalence classes of invertible exact \(\text{Rep}(H)\)-bimodule categories. We discuss the injectivity of this map. We exemplify in the case \(H = T_q\) is a Taft Hopf algebra and for this we classify all exact indecomposable \(\text{Rep}(T_q)\)-bimodule categories.

MSC:
18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
16T05 Hopf algebras and their applications
19D23 Symmetric monoidal categories
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