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تسجيل مستخدم جديدPartial (Co)Actions of Multiplier Hopf Algebras: Morita and Galois Theories
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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.
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In this work we define partial (co)actions on multiplier Hopf algebras, we also present examples and properties. From a partial comodule coalgebra we construct a partial smash coproduct generalizing the constructions made by the L. Delvaux, E. Batista and J. Vercruysse.
In partial action theory, a pertinent question is whenever given a partial (co)action of a Hopf algebra A on an algebra R, it is possible to construct an enveloping (co)action. The authors Alves and Batista, in [2],have shown that this is always poss
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