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Bicrossproducts of multiplier Hopf algebras. (English) Zbl 1244.16025
The aim of the paper is to extend Majid’s bicrossproduct construction to the case of regular multiplier Hopf algebras. If $$A$$ and $$B$$ are two such objects with the property that $$B$$ is a right $$A$$-module algebra and $$A$$ is a left $$B$$-comodule coalgebra, a certain regular multiplier Hopf algebra structure is constructed on the smash product $$A\#B$$. The authors also discuss the dual situation, by starting with two regular multiplier Hopf algebras $$C$$ and $$D$$, such that $$C$$ is a left $$D$$-module algebra, and $$D$$ is a right $$C$$-comodule coalgebra. The *-algebra case is also considered.

##### MSC:
 16T05 Hopf algebras and their applications 16S40 Smash products of general Hopf actions
##### Keywords:
multiplier Hopf algebras; bicrossproducts; smash products
Full Text:
##### References:
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