On the cyclic Homology of multiplier Hopf algebras

In this paper, we will study the theory of cyclic homology for regular multiplier Hopf algebras. We associate a cyclic module to a triple (R, H, X ) consisting of a regular multiplier Hopf algebra H, a left H-comodule algebra R, and a unital left H-module X which is also a unital algebra. First, we construct a paracyclic module to a triple (R, H, X ) and then prove the existence of a cyclic structure associated to this triple.