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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Module categories of finite Hopf algebroids, and self-duality
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by Peter Schauenburg PDF
Trans. Amer. Math. Soc. 369 (2017), 1127-1146 Request permission


We characterize the module categories of suitably finite Hopf algebroids (more precisely, $\times _R$-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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Additional Information
  • Peter Schauenburg
  • Affiliation: Institut de Mathématiques de Bourgogne — UMR 5584 du CNRS, Université de Bourgogne, BP 47870, 21078 Dijon Cedex, France
  • MR Author ID: 346687
  • Email:
  • Received by editor(s): August 13, 2014
  • Received by editor(s) in revised form: February 11, 2015
  • Published electronically: June 20, 2016
  • Additional Notes: This research was partially supported through a FABER Grant by the Conseil régional de Bourgogne
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 1127-1146
  • MSC (2010): Primary 16T99, 18D10
  • DOI:
  • MathSciNet review: 3572267