PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

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

Volume 143 / 2016

Shuangjian Guo, Xiaohui Zhang, Shengxiang Wang Colloquium Mathematicum 143 (2016), 79-103 MSC: Primary 16T05. DOI: 10.4064/cm6509-12-2015 Published online: 3 December 2015

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.

Authors

  • Shuangjian GuoDepartment of Mathematics
    Zhejiang University
    Hangzhou, 310027, P.R. China
    and
    School of Mathematics and Statistics
    Guizhou University of Finance and Economics
    Guiyang, 550025, P.R. China
    e-mail
  • Xiaohui ZhangSchool of Mathematical Sciences
    Qufu Normal University
    Qufu 273165, P.R. China
    e-mail
  • Shengxiang WangSchool of Mathematics and Finance
    Chuzhou University
    Chuzhou 239000, P.R. China
    and
    Department of Mathematics
    Nanjing University
    Nanjing 210093, P.R. China
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image