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.
Keywords
noncommutative differential geometry Hopf cyclic cohomology Hopf algebras flat bundlesMathematics Subject Classifications (2000)
58B34 46L87 46L80Preview
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