Module categories of finite Hopf algebroids, and self-duality
Schauenburg, Peter
HAL, hal-01447298 / Harvested from HAL
Text on HAL
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.
Publié le : 2017-02-04
Classification:  Fusion category,  Finite tensor category,  Rings,  Theorem,  Subfactors,  Bimodules,  Monoidal Categories,  Tensor Categories,  Self-duality,  Weak Hopf algebra,  Hopf algebroid,  MSC: Primary 16T99, 18D10,  [MATH]Mathematics [math] 
@article{hal-01447298,
     author = {Schauenburg, Peter},
     title = {Module categories of finite Hopf algebroids, and self-duality},
     journal = {HAL},
     volume = {2017},
     number = {0},
     year = {2017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01447298}
}

Schauenburg, Peter. Module categories of finite Hopf algebroids, and self-duality. HAL, Tome 2017 (2017) no. 0, . http://gdmltest.u-ga.fr/item/hal-01447298/