On Cores in Yetter-Drinfel'd Hopf Algebras

TL;DR

This paper constructs explicit examples demonstrating that the core of a group-like element in certain Yetter-Drinfel'd Hopf algebras over finite abelian groups can be non-trivial, challenging previous assumptions.

Contribution

It provides explicit examples showing the core can be non-trivial, revealing new structural insights into Yetter-Drinfel'd Hopf algebras.

Findings

The core of a group-like element can be non-trivial in specific Hopf algebra contexts.

Explicit examples illustrate the non-triviality of cores in these algebras.

Abstract

By constructing explicit examples, we show that the core of a group-like element in a cocommutative cosemisimple Yetter-Drinfel'd Hopf algebra over the group ring of a finite abelian group is not always completely trivial.