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Title: Relative Yetter-Drinfeld modules and comodules over braided groups

Let H{sub 1} be a quantum group and f : H{sub 1}⟶H{sub 2} a Hopf algebra homomorphism. Assume that B is some braided group obtained by Majid’s transmutation process. We first show that there is a tensor equivalence between the category of comodules over the braided group B and that of relative Yetter-Drinfeld modules. Next, we prove that the Drinfeld centers of the two categories mentioned above are equivalent to the category of modules over some quantum double, namely, the category of ordinary Yetter-Drinfeld modules over some Radford’s biproduct Hopf algebra. Importantly, the above results not only hold for a finite dimensional quantum group but also for an infinite dimensional one.
Authors:
 [1]
  1. College of Economics and Management, Nanjing Forestry University, 210037 Nanjing (China)
Publication Date:
OSTI Identifier:
22403126
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 4; Other Information: (c) 2015 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; QUANTUM GROUPS; TENSORS; TRANSMUTATION