Partial actions of Hopf algebras can be considered as a generalization of
partial actions of groups on algebras. Among important properties of partial
Hopf actions, it is possible to assure the existence of enveloping actions.
This allows to extend several results from the theory of partial group actions
to the Hopf algebraic setting. In this article, we explore some properties of
the fixed point subalgebra with relations to a partial action of a Hopf
algebra. We also construct, for partial actions of finite dimensional Hopf
algebras a Morita context relating the fixed point subalgebra and the partial
smash product. This is a generalization of a well known result in the theory of
Hopf algebras for the case of partial actions. Finally, we study Hopf-Galois
extensions and reobtain some classical results in the partial case.Comment: revised version with a new section on Partial Hopf-Galois theory
added. To be published in "Algebra and Discrete Mathematics
