Bivariant Hopf cyclic cohomology

Details Bivariant Hopf cyclic cohomology Bivariant Hopf cyclic cohomology

2006-06-14

arxiv.org/abs/math/0606341v1

Mathematics

K-Theory and Homology

21 pages

Scientific paper

For module algebras and module coalgebras over an arbitrary bialgebra, we define two types of bivariant cyclic cohomology groups called bivariant Hopf cyclic cohomology and bivariant equivariant cyclic cohomology. These groups are defined through an extension of Connes' cyclic category $\Lambda$. We show that, in the case of module coalgebras, bivariant Hopf cyclic cohomology specializes to Hopf cyclic cohomology of Connes and Moscovici and its dual version by fixing either one of the variables as the ground field. We also prove an appropriate version of Morita invariance for both of these theories.

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