Invertible bimodule categories over the representation category of a Hopf algebra

2014/02/12 by Femic, Bojana, Castaño, Adriana Mejia, Mombelli, Martin
#16W30 #18D10 #19D23 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1402.2955

Abstract

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

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