Doi Hom-Hopf modules and Frobenius type properties
Volume 148 / 2017
Colloquium Mathematicum 148 (2017), 69-85
MSC: Primary 16T05.
DOI: 10.4064/cm6874-6-2016
Published online: 23 February 2017
Abstract
We continue our study of the category of Doi Hom-Hopf modules introduced by Guo and Zhang [Colloq. Math. 143 (2016), 23–38]. Let $(H, A, C)$ be a Doi Hom-Hopf datum. We find that the forgetful functor $F: \widetilde{\mathscr{H}}(\mathscr{M}_k)(H)^{C}_{A} \rightarrow \widetilde{\mathscr{H}}(\mathscr{M}_k)_{A}$ and its adjoint form a Frobenius pair if and only if (among other equivalent conditions) $AøC$ and $C^{\ast}øA$ are isomorphic as $(A; C^{\ast \rm op}\mathbin{\#} A)$-bimodules.
