Geodesic
Doi Hom-Hopf modules and Frobenius type properties
Huaxi Chen 1   ; Shuangjian Guo 2
1 Department of Mathematics and Physics Bengbu College Bengbu, 233000, P.R. China
2 School of Mathematics and Statistics Guizhou University of Finance and Economics Guiyang, 550025, P.R. China
Colloquium Mathematicum, Tome 148 (2017) no. 1, pp. 69-85 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm6874-6-2016
Keywords: continue study category doi hom hopf modules introduced guo zhang colloq math doi hom hopf datum forgetful functor widetilde mathscr mathscr rightarrow widetilde mathscr mathscr its adjoint form frobenius pair only among other equivalent conditions ast isomorphic ast mathbin bimodules

Huaxi Chen  1   ; Shuangjian Guo  2

1 Department of Mathematics and Physics Bengbu College Bengbu, 233000, P.R. China
2 School of Mathematics and Statistics Guizhou University of Finance and Economics Guiyang, 550025, P.R. China 
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Huaxi Chen; Shuangjian Guo. Doi Hom-Hopf modules and Frobenius type properties. Colloquium Mathematicum, Tome 148 (2017) no. 1, pp. 69-85. doi: 10.4064/cm6874-6-2016

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