A “natural” graded Hopf-algebra and its graded Hopf-cyclic cohomology

Abstract

We prove that the category of differential graded algebras is monoidally equivalent to the category of left graded comodule algebras over a certain graded Hopf algebra. After calculating the graded Hopf-cyclic cohomology of that graded Hopf algebra, we construct cyclic cocycles on any graded differential algebra with a closed graded trace by means of a characteristic homomorphism.