Braided Hopf algebras over non abelian finite groups

TL;DR

This paper surveys the theory of braided Hopf algebras, focusing on tobas over non-abelian finite groups, and discusses their classification and examples in the context of pointed Hopf algebras.

Contribution

It provides a comprehensive overview of tobas within braided Hopf algebras, emphasizing their role in classifying pointed Hopf algebras over non-abelian groups.

Findings

Discussion of tobas from multiple perspectives

Connection to classification problems of pointed Hopf algebras

Presentation of finite-dimensional examples

Abstract

This is a survey of general aspects of the theory of braided Hopf algebras with emphasis on a special class of braided graded Hopf algebras named tobas. The interest on tobas arises from problems of classification of pointed Hopf algebras. We discuss tobas from different points of view following ideas of Lusztig, Nichols and Schauenburg. We then concentrate on braided Hopf algebras in the Yetter-Drinfeld category over H, where H is the group algebra of a non abelian finite group. We present some finite dimensional examples arising in an unpublished work by Milinski and Schneider.