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A generalized double crossproduct for monoidal Hom-Hopf algebras and the Drinfeld double

Volume 146 / 2017

Miman You, Shuanhong Wang Colloquium Mathematicum 146 (2017), 213-238 MSC: Primary 16W30; Secondary 18B40. DOI: 10.4064/cm6633-3-2016 Published online: 3 October 2016

Abstract

A twisted generalization of a double crossproduct called a generalized double Hom-crossproduct is introduced. We give conditions under which this new monoidal Hom-algebra is a monoidal Hom-Hopf algebra. Moreover, its coquasitriangular structure is described. Finally, we also construct a new braided monoidal Hom-category $\widetilde{\mathcal{H}}(_{J}^{J}\operatorname{Mod}^Q_Q)$ obtained from the structure of the generalized double Hom-crossproduct, and establish a kind of new quantum Yang–Baxter Hom-operators.

Authors

  • Miman YouSchool of Mathematics and Information Science
    North China University
    of Resources of Electric Power
    Henan, Zhengzhou 450045, P.R. China
    e-mail
  • Shuanhong WangDepartment of Mathematics
    Southeast University
    Jiangsu, Nanjing 210096, P.R. China
    e-mail

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