A construction of the Hom-Yetter-Drinfeld category

• Autorzy: Haiying Li , Tianshui Ma
• Języki publikacji: EN

Abstrakty

EN

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

Kategorie tematyczne

• 81R50: Quantum groups and related algebraic methods
• 16T05: Hopf algebras and their applications

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 137
• Numer: 1
• Strony: 43-65

Daty

wydano

2014

Twórcy

autor

Haiying Li

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

autor

Tianshui Ma

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

Identyfikatory

DOI

10.4064/cm137-1-4