The core of a group-like element in a cocommutative cosemisimple Yetter-Drinfel'd Hopf algebra over the group ring of Z2×Z2 need not be completely trivial.
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On Cores in Yetter-Drinfel'd Hopf Algebras
The core of a group-like element in a cocommutative cosemisimple Yetter-Drinfel'd Hopf algebra over the group ring of Z2×Z2 need not be completely trivial.