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Gauge Deformations for Hopf Algebras with the Dual Chevalley Property

By ARDIZZONI A., BEATTIE M. and MENINI C.

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 $\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 $

Topics: Hopf algebra, dual Chevalley property, cocycle twist, dual\ud quasi-Hopf algebra.
Year: 2012
DOI identifier: 10.1142/S0219498811005798
OAI identifier: oai:iris.unife.it:11392/1464119
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