Twisted tensor product of multiplier Hopf (∗-)algebras

AbstractWe combine two (not necessarily commutative or co-commutative) multiplier Hopf (∗-)algebras to a new multiplier Hopf (∗-)algebra. We use the construction of a twisted tensor product for algebras, as introduced by A. Van Daele. We then proceed to find sufficient conditions on the twist map for this twisted tensor product to be a multiplier Hopf (∗-)algebra with the natural comultiplication. For usual Hopf algebras, we find that Majid's double crossed product by a matched pair of Hopf algebras is exactly the twisted tensor product Hopf algebra according to an appropriate twist map. Starting from two dually paired multiplier Hopf (∗-)algebras we construct the Drinfel'd double multiplier Hopf algebra in the framework of twisted tensor products