Hopf modules, Frobenius functors and (one-sided) Hopf algebras
arXiv:1904.13065 · doi:10.1016/j.jpaa.2020.106537
Abstract
We investigate the property of being Frobenius for some functors strictly related with Hopf modules over a bialgebra and how this property reflects on the latter. In particular, we characterize one-sided Hopf algebras with anti-(co)multiplicative one-sided antipode as those for which the free Hopf module functor is Frobenius. As a by-product, this leads us to relate the property of being an FH-algebra (in the sense of Pareigis) for a given bialgebra with the property of being Frobenius for certain naturally associated functors.
Author's Accepted Manuscript