On the classification of strongly graded Hopf algebras (Q1614658)

The author studies strong \(G\)-graded bialgebra extensions \(S\) of a bialgebra \(R\). He shows how to extend an antipode of \(R\) to an antipode of \(S\) compatible with the grading. He then investigates the set \(\text{Ext}_k(G,R)\) of isomorphism classes of such Hopf algebras \(S\) and shows \(\text{Ext}_\wp(G,R)\cong H^2_\wp(G,Z(R)^*)\) if the Teichmüller obstruction of the collective character \(\wp\colon G\to\text{Pic}_k(R)\) vanishes. Here \(Z(R)^*\) is the group of all central group-like elements of \(R\).