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arXiv · 1012.4935

Gauge deformations for Hopf algebras with the dual Chevalley property

Alessandro Ardizzoni·Margaret Beattie·Claudia Menini
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Abstract

Let $A$ be a Hopf algebra over a field $K$ of characteristic zero such that its coradical $H$ is a finite dimensional sub-Hopf algebra. Our main theorem shows that there is a gauge transformation $ζ$ on $A$ such that $A^ζ\cong Q#H$ where $A^ζ$ is the dual quasi-bialgebra obtained from $A$ by twisting its multiplication by $ζ$, $Q$ is a connected dual quasi-bialgebra in $^H_H\mathcal{YD}$ and $Q #H $ is a dual quasi-bialgebra called the bosonization of $Q$ by $H$.

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Alessandro Ardizzoni, Margaret Beattie, Claudia Menini. 2011-07-01. Gauge deformations for Hopf algebras with the dual Chevalley property. https://arxiv.org/abs/1012.4935

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