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On the tensor product of bimodule categories over Hopf algebras

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Abstract

Let H be a finite-dimensional Hopf algebra. We give a description of the tensor product of bimodule categories over \(\operatorname {Rep}(H)\). When the bimodule categories are invertible this description can be given explicitly. We present some consequences of this description in the case H is a pointed Hopf algebra.

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Acknowledgements

This work was written in part during a research fellowship granted by CONICET, Argentina in the University of Hamburg, Germany. The author wants to thank the entire staff of Hamburg university and specially to professor Christoph Schweigert, Astrid Dörhöfer and Eva Kuhlmann for the warm hospitality. Thanks are due to the referee for his careful reading and for pointing errors in a previous version of this work.

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  1. Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Medina Allende s/n, (5000) Ciudad Universitaria, Córdoba, Argentina

    Martín Mombelli

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  1. Martín Mombelli
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Correspondence to Martín Mombelli.

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Communicated by I. Runkel.

The work was supported by CONICET, Secyt (UNC), Mincyt (Córdoba) Argentina.

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Mombelli, M. On the tensor product of bimodule categories over Hopf algebras. Abh. Math. Semin. Univ. Hambg. 82, 173–192 (2012). https://doi.org/10.1007/s12188-012-0068-5

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  • DOI: https://doi.org/10.1007/s12188-012-0068-5

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