On Cores in Yetter-Drinfel'd Hopf Algebras
Yevgenia Kashina, Yorck Sommerhaeuser

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.
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