Braided monoidal categories and Doi-Hopf modules for monoidal Hom-Hopf algebras

Shuangjian Guo, Xiaohui Zhang, and Shengxiang Wang. "Braided monoidal categories and Doi-Hopf modules for monoidal Hom-Hopf algebras." Colloquium Mathematicae 143.1 (2016): 79-103. <http://eudml.org/doc/283612>.

@article{ShuangjianGuo2016,
abstract = {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.},
author = {Shuangjian Guo, Xiaohui Zhang, Shengxiang Wang},
journal = {Colloquium Mathematicae},
keywords = {monoidal Hom-Hopf algebra; monoidal category; functor; Doi Hom-Hopf module},
language = {eng},
number = {1},
pages = {79-103},
title = {Braided monoidal categories and Doi-Hopf modules for monoidal Hom-Hopf algebras},
url = {http://eudml.org/doc/283612},
volume = {143},
year = {2016},
}

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 Mathematicae
PY - 2016
VL - 143
IS - 1
SP - 79
EP - 103
AB - 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.
LA - eng
KW - monoidal Hom-Hopf algebra; monoidal category; functor; Doi Hom-Hopf module
UR - http://eudml.org/doc/283612
ER -