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Hopf modules, Frobenius functors and (one-sided) Hopf algebras

par Saracco, Paolo
Référence Journal of pure and applied algebra, 225, 3, 106537
Publication A Paraître, 2021-03-01

Article révisé par les pairs

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Résumé :

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.