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# Module categories of finite Hopf algebroids, and self-duality

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Abstract : We characterize the module categories of suitably finite Hopf algebroids (more precisely, $X_R$-bialgebras in the sense of Takeuchi (1977) that are Hopf and finite in the sense of a work by the author (2000)) as those $k$-linear abelian monoidal categories that are module categories of some algebra, and admit dual objects for "sufficiently many" of their objects. Then we proceed to show that in many situations the Hopf algebroid can be chosen to be self-dual, in a sense to be made precise. This generalizes a result of Pfeiffer for pivotal fusion categories and the weak Hopf algebras associated to them.
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01447298
Contributeur : Imb - Université de Bourgogne <>
Soumis le : jeudi 26 janvier 2017 - 17:29:28
Dernière modification le : vendredi 23 avril 2021 - 09:28:02

### Citation

Peter Schauenburg. Module categories of finite Hopf algebroids, and self-duality. Transactions of the American Mathematical Society, American Mathematical Society, 2017, 369 (2), pp.1127 - 1146. ⟨10.1090/tran6687⟩. ⟨hal-01447298⟩

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