Braided monoidal categories and Doi–Hopf modules for monoidal Hom-Hopf algebras
Colloquium Mathematicum, Tome 143 (2016) no. 1, pp. 79-103
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We continue our study of the category of Doi Hom-Hopf modules introduced in [Colloq. Math., to appear]. We find a sufficient condition for the category of Doi Hom-Hopf modules to be monoidal. We also obtain a condition for a monoidal Hom-algebra and monoidal Hom-coalgebra to be monoidal Hom-bialgebras. Moreover, we introduce morphisms between the underlying monoidal Hom-Hopf algebras, Hom-comodule algebras and Hom-module coalgebras, which give rise to functors between the category of Doi Hom-Hopf modules, and we study tensor identities for monodial categories of Doi Hom-Hopf modules. Furthermore, we construct a braiding on the category of Doi Hom-Hopf modules. Finally, as an application of our theory, we get a braiding on the category of Hom-modules, on the category of Hom-comodules, and on the category of Hom-Yetter–Drinfeld modules.
Keywords:
continue study category doi hom hopf modules introduced colloq math appear sufficient condition category doi hom hopf modules monoidal obtain condition monoidal hom algebra monoidal hom coalgebra monoidal hom bialgebras moreover introduce morphisms between underlying monoidal hom hopf algebras hom comodule algebras hom module coalgebras which rise functors between category doi hom hopf modules study tensor identities monodial categories doi hom hopf modules furthermore construct braiding category doi hom hopf modules finally application theory get braiding category hom modules category hom comodules category hom yetter drinfeld modules
Affiliations des auteurs :
Shuangjian Guo 1 ; Xiaohui Zhang 2 ; Shengxiang Wang 3
@article{10_4064_cm6509_12_2015,
author = {Shuangjian Guo and Xiaohui Zhang and Shengxiang Wang},
title = {Braided monoidal categories and {Doi{\textendash}Hopf} modules for monoidal {Hom-Hopf} algebras},
journal = {Colloquium Mathematicum},
pages = {79--103},
publisher = {mathdoc},
volume = {143},
number = {1},
year = {2016},
doi = {10.4064/cm6509-12-2015},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm6509-12-2015/}
}
TY - JOUR AU - Shuangjian Guo AU - Xiaohui Zhang AU - Shengxiang Wang TI - Braided monoidal categories and Doi–Hopf modules for monoidal Hom-Hopf algebras JO - Colloquium Mathematicum PY - 2016 SP - 79 EP - 103 VL - 143 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/cm6509-12-2015/ DO - 10.4064/cm6509-12-2015 LA - en ID - 10_4064_cm6509_12_2015 ER -
%0 Journal Article %A Shuangjian Guo %A Xiaohui Zhang %A Shengxiang Wang %T Braided monoidal categories and Doi–Hopf modules for monoidal Hom-Hopf algebras %J Colloquium Mathematicum %D 2016 %P 79-103 %V 143 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/cm6509-12-2015/ %R 10.4064/cm6509-12-2015 %G en %F 10_4064_cm6509_12_2015
Shuangjian Guo; Xiaohui Zhang; Shengxiang Wang. Braided monoidal categories and Doi–Hopf modules for monoidal Hom-Hopf algebras. Colloquium Mathematicum, Tome 143 (2016) no. 1, pp. 79-103. doi: 10.4064/cm6509-12-2015
Cité par Sources :