Measurings of Hopf algebroids and morphisms in cyclic (co)homology theories

Abstract

In this paper, we consider measurings between Hopf algebroids and show that they induce morphisms on cyclic homology and cyclic cohomology. We also consider comodule measurings between SAYD modules over Hopf algebroids. These measurings induce morphisms on cyclic (co)homology of Hopf algebroids with SAYD coefficients. Finally, we obtain morphisms on cyclic homology induced by measurings of cyclic comp modules over operads with multiplication