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Partial representations of connected and smash product Hopf algebras
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abstract
We show that every partial representation of a connected Hopf algebra is global. Some interesting classes of partial representations of smash product Hopf algebras are studied, and a description of the partial "Hopf" algebra if the first tensorand is connected is given. If $H$ is cocommutative and has finitely many grouplikes, this allows to see $H_{par}$ as the weak Hopf algebra coming from a Hopf category.
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Cited by 2 Pith papers
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Globalization and the biactegory of partial modules
Partial H-modules form a biactegory over H-modules, and for pointed Hopf algebras with finitely many grouplikes the standard dilation functor is naturally isomorphic to the Hom-object {Apar, -}.
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On partial representations of pointed Hopf algebras
For pointed Hopf algebras with finite grouplikes and invertible antipode, the partial representation algebra H_par decomposes as a direct sum of unital ideals indexed by the components of the groupoid associated to th...
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