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arXiv · 1402.2955

Invertible bimodule categories over the representation category of a Hopf algebra

Bojana Femic·Adriana Mejia Castaño·Martin Mombelli
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Abstract

For any finite-dimensional Hopf algebra $H$ we construct a group homomorphism $\biga(H)\to \text{BrPic}(\Rep(H))$, 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 $H=T_q$ is a Taft Hopf algebra and for this we classify all exact indecomposable $\Rep(T_q)$-bimodule categories.

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Bojana Femic, Adriana Mejia Castaño, Martin Mombelli. 2014-02-12. Invertible bimodule categories over the representation category of a Hopf algebra. https://arxiv.org/abs/1402.2955

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