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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
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