Relative Yetter-Drinfeld modules and comodules over braided groups

Journal Article · Wed Apr 15 00:00:00 EDT 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4918773· OSTI ID:22403126

Zhu, Haixing ^[1]

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1. College of Economics and Management, Nanjing Forestry University, 210037 Nanjing (China)

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.

• OSTI ID: 22403126
• Journal Information: Journal of Mathematical Physics, Vol. 56, Issue 4; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
QUANTUM GROUPS
TENSORS
TRANSMUTATION