@article { author = {Haghighatdoost, Ghorbanali and Abbasi Makrani, Hami and Mahjoubi, Rasoul}, title = {On the cyclic Homology of multiplier Hopf algebras}, journal = {Sahand Communications in Mathematical Analysis}, volume = {09}, number = {1}, pages = {113-128}, year = {2018}, publisher = {University of Maragheh}, issn = {2322-5807}, eissn = {2423-3900}, doi = {10.22130/scma.2018.23645}, abstract = {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.}, keywords = {Multiplier Hopf algebra,Cyclic homology,Cyclic module,Paracyclic module,$H-$comodule,$H-$module}, url = {https://scma.maragheh.ac.ir/article_23645.html}, eprint = {https://scma.maragheh.ac.ir/article_23645_980a6fd18602b47503b690dd49acad52.pdf} }