Partial (Co)Actions of Multiplier Hopf Algebras: Morita and Galois Theories

Abstract: In this work we deal with partial (co)action of multiplier Hopf algebras on not necessarily unital algebras. Our main goal is to construct a Morita context relating the coinvariant algebra $R^{\underline{coA}}$ with a certain subalgebra of the smash product $R#\widehat{A}$. Besides this we present the notion of partial Galois coaction, which is closely related to this Morita context.