Enveloping Actions for Partial Hopf Actions

Details Enveloping Actions for Partial Hopf Actions Enveloping Actions for Partial Hopf Actions

2008-05-30

arxiv.org/abs/0805.4805v2

Mathematics

Rings and Algebras

27 pages; revised version with minor corrections, mainly typos

Scientific paper

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.

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