Would you please give some references concerning the number of indecomposable modules over preprojective algebras of type $A\_n$?


More precisely, I need references about the following claim: The number of indecomposable modules over the preprojective algebra of type $A\_n$ is:


1) only one for $n=1$, 


2) four for $n=2$, 


3) $12$ for $n=3$, 


4) $40$ for $n=4$, and


5) an infinite number of indecomposable modules for $n\geq5$. 



Indecomposable modules over preprojective algebras
This is stated in [Rigid modules over preprojective algebras](http://www.math.uni-bonn.de/~schroer/preprints/rigid.pdf) by Geiss, Leclerc and Schröer, Sections 8.1-8.3. As noted in my comment a proof of the $n=5$ statement can be found in [The module theoretic approach to quasi-hereditary algebras](http://www.mathematik.uni-bielefeld.de/~ringel/opus/good-d-r.pdf). (These are of course not the original references, I doubt that there is one original reference)
Note also that you can split up the $n\geq 5$ case in $n=5$, which is the tame case, i.e. there is a classification of the infinitely many indecomposable modules, and the $n>5$ case, where a classification is not possible.


EDIT: There is a proof in [Semicanonical bases and preprojective algebras](http://arxiv.org/PS_cache/math/pdf/0402/0402448v2.pdf) by Geiss, Leclerc, Schröer, Section 9, via the theory of Galois coverings. The Auslander-Reiten quiver of these algebras can also be found there. The statement was long before and is probably part of the folklore in the representation theory of quivers.


