Document Type: Research Paper


Department of Mathematics, Faculty of Science, Azarbaijan shahid Madani university, Tabriz, Iran.


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


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