Cup products in Hopf cyclic cohomology via cyclic modules

Abstract

We redefine the cup products in Hopf cyclic cohomology. These cup products were first defined by the author and M. Khalkhali via a relatively complicated method as a generalization of Connes' cup product for cyclic cohomology of algebras. In this paper we use the generalized Eilenberg-Zilber theorem and define the cup product using a bicocyclic module naturally associated to the cocyclic modules of the coalgebras and the algebras in question. In the last part of the paper we derive some formulas for the cup products.