  We study the problem of classifying triangulated categories with
finite-dimensional morphism spaces and finitely many indecomposables over an
algebraically closed field. We obtain a new proof of the following result due
to Xiao and Zhu: the Auslander-Reiten quiver of such a category is of the form
$\mathbb{Z}\Delta/G$ where $\Delta$ is a disjoint union of simply laced Dynkin
diagrams and $G$ a weakly admissible group of automorphisms of
$\mathbb{Z}\Delta$. Then we prove that for `most' groups $G$, the category $\T$
is standard, \emph{i.e.} $k$-linearly equivalent to an orbit category
$\mathcal{D}^b(\modd k\Delta)/\Phi$. This happens in particular when $\T$ is
maximal $d$-Calabi-Yau with $d\geq2$. Moreover, if $\T$ is standard and
algebraic, we can even construct a triangle equivalence between $\T$ and the
corresponding orbit category. Finally we give a sufficient condition for the
category of projectives of a Frobenius category to be triangulated. This allows
us to construct non standard 1-Calabi-Yau categories using deformed
preprojective algebras of generalized Dynkin type.
