Enveloping Actions for Partial Hopf Actions
By Marcelo Muniz Silva Alves, Eliezer Batista. 2008
68 citations recorded by the source corpus.
Motivated by partial group actions on unital algebras, in this article we extend many results obtained by Exel and Dokuchaev to the context of partial actions of Hopf algebras, according to Caenepeel and Jansen. First, we generalize the theorem about the existence of an enveloping action, also known as the globalization theorem. Second, we construct a Morita context between the partial smash product and the smash product related to the enveloping action. Third, we dualize the globalization theorem to partial coactions and finally, we define partial representations of Hopf algebras and show some results relating partial actions and partial representations.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/79d23b77bafdb398a703bb24aacfe1ac914708ab
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Recent developments around partial actions (2018, background): “The concept of a partial group representation was extended to that of a partial representations of a Hopf algebra in [18] and [22].”