  We present a detailed computation of the cyclic and the Hochschild homology
and cohomology of generic and 3-Calabi-Yau homogeneous down-up algebras. This
family was defined by Benkart and Roby in their study of differential posets.
Our calculations are completely explicit, by making use of the Koszul bimodule
resolution and arguments similar to those used by the second and third authors
for Yang-Mills algebras.
