  A triangulated category is said to be Calabi-Yau of dimension d if the dth
power of its suspension is a Serre functor. We determine which stable
categories of self-injective algebras A of finite representation type are
Calabi-Yau and compute their Calabi-Yau dimensions. We achieve this by studying
the minimal projective resolution of the stable Auslander algebra of A over its
enveloping algebra, and use covering theory to reduce to (generalized)
preprojective algebras of Dynkin graphs. We also describe how this problem can
be approached by realizing the stable categories in question as orbit
categories of the bounded derived categories of hereditary algebras.
