Globalization of twisted partial Hopf actions
Journal of the Australian Mathematical Society, 2016•cambridge.org
… We start with the concept of a partial measuring map of a bialgebra (or Hopf algebra) H
on a unital algebra A, giving, in our examples, a complete characterization of these maps in
the case of H being the group algebra κG, the dual (κG)∗ of the group algebra κG of a finite
group G, and the Sweedler Hopf algebra H4 and A coinciding (in all three cases) with the
base field κ. Then we proceed with the concept of a twisted partial action of a Hopf algebra (or,
more generally, a bialgebra), in which we include all properties needed to guarantee that …
on a unital algebra A, giving, in our examples, a complete characterization of these maps in
the case of H being the group algebra κG, the dual (κG)∗ of the group algebra κG of a finite
group G, and the Sweedler Hopf algebra H4 and A coinciding (in all three cases) with the
base field κ. Then we proceed with the concept of a twisted partial action of a Hopf algebra (or,
more generally, a bialgebra), in which we include all properties needed to guarantee that …
In this work, we review some properties of twisted partial actions of Hopf algebras on unital algebras and give necessary and sufficient conditions for a twisted partial action to have a globalization. We also elaborate a series of examples.
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