  In this report we give an intrinsic treatment of the results we developed in
a previous work connecting the differential calculi on Hopf algebras to the
Drinfeld double. In the first place we recover that bicovariant bimodules are
in one to one correspondence with the Drinfeld double representations; we then
introduce a Hochschild cohomology of the algebra of functions and discuss the
main result stating that each differential calculus is associated to a
1-cocycle satisfying an additional invariance condition with respect to a
natural action. Defining a Hochschild cohomology of the double, the above
invariance becomes a condition with respect to the enveloping algebra component
of the double that must be added to the 1-cocycle relation.
