Homology, Homotopy and Applications

Volume 10 (2008)

Number 2

Cup products in Hopf cyclic cohomology via cyclic modules

Pages: 273 – 286

DOI: http://dx.doi.org/10.4310/HHA.2008.v10.n2.a14


Bahram Rangipour (Department of Mathematics and Statistics, University of New Brunswick, Fredericton, N.B., Canada)


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.


cup product; Hopf cyclic cohomology

2010 Mathematics Subject Classification

16E40, 19D55

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