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The fundamental theorem and Maschke’s theorem in the category of relative Hom-Hopf modules

Volume 144 / 2016

Yuanyuan Chen, Zhongwei Wang, Liangyun Zhang Colloquium Mathematicum 144 (2016), 55-71 MSC: 16T05, 16T25, 17A30. DOI: 10.4064/cm6514-11-2015 Published online: 17 February 2016

Abstract

We introduce the concept of relative Hom-Hopf modules and investigate their structure in a monoidal category $\widetilde{\mathcal{H}}(\mathcal{M}_{k})$. More particularly, the fundamental theorem for relative Hom-Hopf modules is proved under the assumption that the Hom-comodule algebra is cleft. Moreover, Maschke’s theorem for relative Hom-Hopf modules is established when there is a multiplicative total Hom-integral.

Authors

  • Yuanyuan ChenCollege of Science
    Nanjing Agricultural University
    Nanjing 210095, P.R. China
  • Zhongwei WangDepartment of Basic Science
    Jinling Institute of Technology
    Nanjing 210069, P.R. China
  • Liangyun ZhangCollege of Science
    Nanjing Agricultural University
    Nanjing 210095, P.R. China
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