New techniques for pointed Hopf algebras

TL;DR

This paper introduces new techniques to determine when the dimension of certain pointed Hopf algebras linked to non-abelian groups is infinite, building on prior work and demonstrating applications.

Contribution

The paper develops novel methods for analyzing the dimensionality of pointed Hopf algebras associated with non-abelian groups, extending existing theoretical frameworks.

Findings

Techniques to identify infinite-dimensional pointed Hopf algebras

Applications demonstrating the effectiveness of the methods

Connections to previous foundational results

Abstract

We present techniques that allow to decide that the dimension of some pointed Hopf algebras associated with non-abelian groups is infinite. These results are consequences of arXiv:0803.2430v1. We illustrate each technique with applications.