Hopf modules and noncommutative differential geometry

Kaygun A. , KHALKHALI M.

LETTERS IN MATHEMATICAL PHYSICS, cilt.76, sa.1, ss.77-91, 2006 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 76 Konu: 1
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1007/s11005-006-0062-x
  • Dergi Adı: LETTERS IN MATHEMATICAL PHYSICS
  • Sayfa Sayıları: ss.77-91

Özet

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.