Semi-direct products of multiplier Hopf algebras: Smash products

Abstract

The well-known concept of smash product, and the dual notion of smash coproduct were first formulated by Molnar for Hopf algebras. The object of this paper is to extend the theory of smash products 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 product and we obtain results in the *-situation.