Hopf modules and noncommutative differential geometry

Atabey Kaygun*, Masoud Khalkhali

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

2 Citations (Scopus)


We define a new algebra of noncommutative differential forms for any Hopf algebra with an invertible antipode. We prove that there is a one-to-one correspondence between anti-Yetter-Drinfeld modules, which serve as coefficients for the Hopf cyclic (co)homology, and modules which admit a flat connection with respect to our differential calculus. Thus, we show that these coefficient modules can be regarded as "flat bundles" in the sense of Connes' noncommutative differential geometry.

Original languageEnglish
Pages (from-to)77-91
Number of pages15
JournalLetters in Mathematical Physics
Issue number1
Publication statusPublished - Apr 2006
Externally publishedYes


  • Flat bundles
  • Hopf algebras
  • Hopf cyclic cohomology
  • Noncommutative differential geometry


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