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Title: Radford's biproducts and Yetter-Drinfeld modules for monoidal Hom-Hopf algebras

Let (H, α) be a monoidal Hom-bialgebra and (B, β) be a left (H, α)-Hom-module algebra and also a left (H, α)-Hom-comodule coalgebra. Then in this paper, we first introduce the notion of a Hom-smash coproduct, which is a monoidal Hom-coalgebra. Second, we find sufficient and necessary conditions for the Hom-smash product algebra structure and the Hom-smash coproduct coalgebra structure on B ⊗ H to afford B ⊗ H a monoidal Hom-bialgebra structure, generalizing the well-known Radford's biproduct, where the conditions are equivalent to that (B, β) is a bialgebra in the category of Hom-Yetter-Drinfeld modules H/H HYD. Finally, we illustrate the category of Hom-Yetter-Drinfeld modules H/H HYD and prove that the category H/H HYD is a braided monoidal category.
Authors:
 [1] ;  [2]
  1. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004 (China)
  2. Shanghai University of Finance and Economics Zhejiang College, Jinhua 321013 (China)
Publication Date:
OSTI Identifier:
22251163
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; MATHEMATICAL OPERATORS; TENSORS