Products in Hopf-Cyclic Cohomology

Details Products in Hopf-Cyclic Cohomology Products in Hopf-Cyclic Cohomology

2007-10-12

arxiv.org/abs/0710.2559v1

Mathematics

K-Theory and Homology

15 pages

Scientific paper

We construct several pairings in Hopf-cyclic cohomology of (co)module (co)algebras with arbitrary coefficients. The key ideas instrumental in constructing these pairings are the derived functor interpretation of Hopf-cyclic and equivariant cyclic (co)homology, and the Yoneda interpretation of Ext-groups. As a special case of one of these pairings, we recover the Connes-Moscovici characteristic map in Hopf-cyclic cohomology. We also prove that this particular pairing, along with few others, would stay the same if we replace the derived category of (co)cyclic modules with the homotopy category of (special) towers of $X$-complexes, or the derived category of mixed complexes.

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