Invertible bimodule categories over the representation category of a Hopf algebra
For any finite-dimensional Hopf algebra H we construct a group homomorphism BiGal (H) → BrPic(Rep(H)), from the group of equivalence classes of H-biGalois objects to the group of equivalence classes of invertible exact Rep(H)-bimodule categories. We discuss the injectivity of this map. We exemplify in the case H = Tq is a Taft Hopf algebra and for this we classify all exact indecomposable Rep(Tq)- bimodule categories.
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| Main Authors: | , , |
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| Format: | article biblioteca |
| Language: | eng |
| Published: |
2014-02-12
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| Subjects: | Categorías tensoriales, Álgebras de Hopf, Representaciones de categorías tensoriales, Grupo de Brauer-Picard, Monoidal categories, Symmetric monoidal categories, Brauer-Picard group, Tensor category, biGalois object, |
| Online Access: | http://hdl.handle.net/11086/28253 https://doi.org/10.48550/arXiv.1402.2955 |
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| Summary: | For any finite-dimensional Hopf algebra H we construct a group homomorphism
BiGal (H) → BrPic(Rep(H)), from the group of equivalence classes of H-biGalois
objects to the group of equivalence classes of invertible exact Rep(H)-bimodule
categories. We discuss the injectivity of this map. We exemplify in the case H = Tq
is a Taft Hopf algebra and for this we classify all exact indecomposable Rep(Tq)-
bimodule categories. |
|---|