Hopf cocycles associated to pointed and copointed deformations over S3

Abstract

The algebras in the classification of finite dimensional pointed and copointed Hopf algebras over the symmetric group on three letters are all Hopf cocycle deformations of their associated graded objects. We show that these cocycles are generically pure, namely they are not co-homologous to exponentials of Hochschild 2-cocycles; apart from very specific examples. We provide a full description of these cocycles on a given basis.