Gauge deformations for Hopf algebras with the dual Chevalley property. (Q2892991)

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. Then, the Hopf algebra \(A\) has the dual Chevalley property. In this paper, the authors mainly show 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 \(^H_H\mathcal {YD}\) (the category of left Yetter-Drinfel'd modules) and \(Q\#H\) is a dual quasi-bialgebra called the bosonization of \(Q\) by \(H\).