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Drinfeld Codoubles of Hom–Hopf Algebras

  • Xiaohui Zhang
  • Shuangjian Guo
  • Shengxiang WangEmail author
Article
  • 13 Downloads

Abstract

The main purpose of the present paper is to develop the theory of center constructions on Hom–Hopf algebras. Let H be a Hom–Hopf algebra, we first introduce the notions of nth Yetter–Drinfeld modules and mth Drinfeld codouble for H. Also we prove that the category \({\mathcal {YD}}_H^H(n)\) of nth Yetter–Drinfeld modules of H is a braided autonomous category. Finally, we show that \({\mathcal {YD}}_H^H(n)\) and \(Corep^{i,j}(CD_m(H))\) (i.e., the corepresentation category of the Drinfeld codouble of H) are braided isomorphic as the full subcategories of \(Corep^{i,j}(H)\).

Keywords

Hom–Hopf algebra Yetter–Drinfeld module Category center Drinfeld codouble 

Mathematics Subject Classification

16T15 16W30 

Notes

Acknowledgements

The work of X. H. Zhang is supported by the NSF of China (Nos. 11801304, 11801306) and the Project Funded by China Postdoctoral Science Foundation (No. 2018M630768). The work of S. J. Guo is supported by the NSF of China (No. 11761017). The work of S. X.Wang is supported by the outstanding topnotch talent cultivation project of Anhui Province (No. gxfx2017123) and the Anhui Provincial Natural Science Foundation (1808085MA14).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesQufu Normal UniversityQufuPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsGuizhou University of Finance and EconomicsGuiyangPeople’s Republic of China
  3. 3.School of Mathematics SciencesChuzhou UniversityChuzhouPeople’s Republic of China

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