Hopf cocycles associated to pointed and copointed deformations over S3

TL;DR

This paper explicitly describes Hopf 2-cocycles relevant to classifying finite-dimensional pointed and copointed Hopf algebras over S3, distinguishing between exponential and pure cocycles.

Contribution

It provides an explicit classification of Hopf 2-cocycles over S3, clarifying their structure and properties in the context of pointed and copointed Hopf algebras.

Findings

Identifies which cocycles are exponentials of Hochschild 2-cocycles

Determines which cocycles are pure

Provides explicit descriptions of the cocycles

Abstract

We present an explicit description of the Hopf 2-cocycles involved in the classification of finite dimensional pointed and copointed Hopf algebras over the symmetric group on three letters. We determine which cocycles are exponentials of Hochschild 2-cocycles and which ones are pure.