Yetter-Drinfeld modules over bosonizations of dually paired Hopf algebras

Abstract

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

45 pages

References in corpus (1)

• Construction of quantized enveloping algebras by cocycle deformation

Cited by in corpus (2)

• Logarithmic ^sl(2) CFT models from Nichols algebras. 1
• Algebras of Non-Local Screenings and Diagonal Nichols Algebras