Gauge deformations for Hopf algebras with the dual Chevalley property

Details Gauge deformations for Hopf algebras with the dual Chevalley property Gauge deformations for Hopf algebras with the dual Chevalley property

2010-12-22

arxiv.org/abs/1012.4935v2

Mathematics

Quantum Algebra

Scientific paper

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 $\zeta $ on $A$ such that $A^{\zeta}\cong Q#H$ where $A^\zeta$ is the dual quasi-bialgebra obtained from $A$ by twisting its multiplication by $\zeta$, $Q$ 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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