A construction of the Hom-Yetter–Drinfeld category

Haiying Li ¹   ; Tianshui Ma ¹

¹ College of Mathematics and Information Science Henan Normal University 453007 Xinxiang, China

Colloquium Mathematicum, Tome 137 (2014) no. 1, pp. 43-65

Résumé

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.

Détail

DOI : 10.4064/cm137-1-4

Keywords: continuation recent work about smash product hom hopf algebras colloq math introduce hom yetter drinfeld category mathbb via radford biproduct hom hopf algebra prove hom yetter drinfeld modules provide solutions hom yang baxter equation mathbb pre braided tensor category where beta hom hopf algebra furthermore natural diamond alpha otimes beta radford biproduct hom hopf algebra only alpha hom hopf algebra category mathbb finally examples applications given