Bivariant hopf cyclic cohomology

Atabey Kaygun, Masoud Khalkhali*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 Λ. 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.

Original languageEnglish
Pages (from-to)2513-2537
Number of pages25
JournalCommunications in Algebra
Issue number7
Publication statusPublished - Jul 2010
Externally publishedYes


  • Bivariant cyclic cohomology
  • Conne's cyclic category
  • Cyclic duality
  • Hopf algebra
  • Hopf-cyclic cohomology


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