Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



Module categories of finite Hopf algebroids, and self-duality

Author: Peter Schauenburg
Journal: Trans. Amer. Math. Soc. 369 (2017), 1127-1146
MSC (2010): Primary 16T99, 18D10
Published electronically: June 20, 2016
MathSciNet review: 3572267
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: 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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 16T99, 18D10

Retrieve articles in all journals with MSC (2010): 16T99, 18D10

Additional Information

Peter Schauenburg
Affiliation: Institut de Mathématiques de Bourgogne — UMR 5584 du CNRS, Université de Bourgogne, BP 47870, 21078 Dijon Cedex, France

Keywords: Finite tensor category, fusion category, Hopf algebroid, weak Hopf algebra, self-duality
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
Article copyright: © Copyright 2016 American Mathematical Society