Hopf modules and noncommutative differential geometry


Kaygun A. , KHALKHALI M.

LETTERS IN MATHEMATICAL PHYSICS, vol.76, no.1, pp.77-91, 2006 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 76 Issue: 1
  • Publication Date: 2006
  • Doi Number: 10.1007/s11005-006-0062-x
  • Title of Journal : LETTERS IN MATHEMATICAL PHYSICS
  • Page Numbers: pp.77-91

Abstract

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.