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arXiv · 1904.13065

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

Paolo Saracco
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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.

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Paolo Saracco. 2019-04-30. Hopf modules, Frobenius functors and (one-sided) Hopf algebras. https://doi.org/10.1016/j.jpaa.2020.106537

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