Yetter-Drinfeld modules over bosonizations of dually paired Hopf algebras

Details Yetter-Drinfeld modules over bosonizations of dually paired Hopf algebras Yetter-Drinfeld modules over bosonizations of dually paired Hopf algebras

2011-11-20

arxiv.org/abs/1111.4673v1

Mathematics

Quantum Algebra

45 pages

Scientific paper

Let $(R^{\vee},R)$ 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 $R^{\vee}$, respectively. As an application of this very general category isomorphism we obtain a natural proof of the existence of reflections of Nichols algebras of semisimple Yetter-Drinfeld modules over $H$. Key words: Hopf algebras, quantum groups, Weyl groupoid

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