Semi-direct products of multiplier Hopf algebras: Smash coproducts

Abstract

The construction of the smash coproduct of two Hopf algebras, as the dual notion of smash product, was first formulated by Molnar. In this paper we extend this theory to multiplier Hopf algebras. We prove that the result of Molnar is still true for regular multiplier Hopf algebras under an appropriate form. We consider integrals on the smash coproduct and we obtain results in the *-situation.