On the cyclic Homology of multiplier Hopf algebras (original) (raw)

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