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A construction of the Hom-Yetter–Drinfeld category

Volume 137 / 2014

Haiying Li, Tianshui Ma Colloquium Mathematicum 137 (2014), 43-65 MSC: 16T05, 81R50. DOI: 10.4064/cm137-1-4

Abstract

In continuation of our recent work about smash product Hom-Hopf algebras [Colloq. Math. 134 (2014)], we introduce the Hom-Yetter–Drinfeld category $_H^H{\mathbb {YD}}$ via the Radford biproduct Hom-Hopf algebra, and prove that Hom-Yetter–Drinfeld modules can provide solutions of the Hom-Yang–Baxter equation and $_H^H{\mathbb {YD}}$ is a pre-braided tensor category, where $(H, \beta , S)$ is a Hom-Hopf algebra. Furthermore, we show that $(A^{\natural }_{\diamond } H,\alpha \otimes \beta )$ is a Radford biproduct Hom-Hopf algebra if and only if $(A,\alpha )$ is a Hom-Hopf algebra in the category $_H^H{\mathbb {YD}}$. Finally, some examples and applications are given.

Authors

  • Haiying LiCollege of Mathematics and Information Science
    Henan Normal University
    453007 Xinxiang, China
    e-mail
  • Tianshui MaCollege of Mathematics and Information Science
    Henan Normal University
    453007 Xinxiang, China
    e-mail

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