GAUGE DEFORMATIONS FOR HOPF ALGEBRAS WITH THE DUAL CHEVALLEY PROPERTY

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 Aζ ≅ Q#H where Aζ is the dual quasi-bialgebra obtained from A by twisting its multiplication by ζ, Q is a connected dual quasi-bialgebra in [Formula: see text] and Q#H is a dual quasi-bialgebra called the bosonization of Q by H.