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arXiv · 1402.2214

Partially dualized Hopf algebras have equivalent Yetter-Drinfel'd modules

Alexander Barvels·Simon Lentner·Christoph Schweigert
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Abstract

Given a Hopf algebra $H$ and a projection $H\to A$ to a Hopf subalgebra, we construct a Hopf algebra $r(H)$, called the partial dualization of $H$, with a projection to the Hopf algebra dual to $A$. This construction provides powerful techniques in the general setting of braided monoidal categories. The construction comprises in particular the reflections of generalized quantum groups, arxiv:1111.4673 . We prove a braided equivalence between the Yetter-Drinfel'd modules over a Hopf algebra and its partial dualization.

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BibTeXRIS

Alexander Barvels, Simon Lentner, Christoph Schweigert. 2014-02-10. Partially dualized Hopf algebras have equivalent Yetter-Drinfel'd modules. https://arxiv.org/abs/1402.2214

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