1Department of Mathematics and Physics Bengbu College Bengbu, 233000, P.R. China 2School 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
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.
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
Affiliations des auteurs :
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
