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

New braided monoidal categories over monoidal Hom-Hopf algebras

Volume 146 / 2017

Shengxiang Wang, Nanqing Ding Colloquium Mathematicum 146 (2017), 77-97 MSC: 16A10, 16W30. DOI: 10.4064/cm6706-11-2015 Published online: 25 August 2016

Abstract

Let $(H,\alpha )$ and $(B,\beta )$ be two monoidal Hom-Hopf algebras. We introduce the notion of a generalized Hom-Long dimodule and show that the category $^{B}_{H}\mathcal {L}$ of generalized Hom-Long dimodules is an autonomous category. We prove that $^{B}_{H}\mathcal {L}$ is a braided monoidal category if $(H,\alpha )$ is quasitriangular and $(B,\beta )$ is coquasitriangular, and we show that $^{B}_{H}\mathcal {L}$ is a subcategory of the Hom-Yetter–Drinfeld category $^{H\otimes B}_{H\otimes B}\mathcal {HYD}$. Moreover, we prove that the category of Hom-modules (resp., Hom-comodules) over a triangular (resp., cotriangular) Hom-Hopf algebra contains a symmetric generalized Hom-Long dimodule category.

Authors

  • Shengxiang WangDepartment of Mathematics
    Nanjing University
    Nanjing, 210093, P.R. China
    and
    School of Mathematics and Finance
    Chuzhou University
    Chuzhou, 239000, P.R. China
    e-mail
  • Nanqing DingDepartment 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