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.