  We show by a direct computation that, for any Hopf algebra with a
modulus-like character, the formulas first introduced in [CM] in the context of
characteristic classes for actions of Hopf algebras, do define a cyclic module.
This provides a natural generalization of Lie algebra cohomology to the general
framework of Noncommutative Geometry, which covers the case of the Hopf algebra
associated to n-dimensional transverse geometry [CM] as well as the function
algebras of the classical quantum groups.
