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Abstract: Partial actions of Hopf algebras can be considered as a generalization ofpartial actions of groups on algebras. Among important properties of partialHopf actions, it is possible to assure the existence of enveloping actions.This allows to extend several results from the theory of partial group actionsto the Hopf algebraic setting. In this article, we explore some properties ofthe fixed point subalgebra with relations to a partial action of a Hopfalgebra. We also construct, for partial actions of finite dimensional Hopfalgebras a Morita context relating the fixed point subalgebra and the partialsmash product. This is a generalization of a well known result in the theory ofHopf algebras for the case of partial actions. Finally, we study Hopf-Galoisextensions and reobtain some classical results in the partial case.



Author: Marcelo Muniz S. Alves, Eliezer Batista

Source: https://arxiv.org/



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