Yetter–Drinfeld modules over bosonizations of dually paired Hopf algebras

Let (R∨,R) be a dual pair of Hopf algebras in the category of Yetter–Drinfeld modules over a Hopf algebra H with bijective antipode. We show that there is a braided monoidal isomorphism between rational left Yetter–Drinfeld modules over the bosonizations of R and of R∨, respectively. As an applicati...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2013-09, Vol.244, p.354-394
Main Authors: Heckenberger, I., Schneider, H.-J.
Format: Article
Language:English
Subjects:
Hopf algebras
Quantum groups
Weyl groupoid
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Summary:Let (R∨,R) be a dual pair of Hopf algebras in the category of Yetter–Drinfeld modules over a Hopf algebra H with bijective antipode. We show that there is a braided monoidal isomorphism between rational left Yetter–Drinfeld modules over the bosonizations of R and of R∨, respectively. As an application of this very general category isomorphism we obtain a natural proof of the existence of reflections of Nichols algebras of semi-simple Yetter–Drinfeld modules over H.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2013.05.009