Given a connected quiver algebra $A$ over a finite field $K$.



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> Question : Is there an effective/quick method to obtain all $d$-dimensional indecomposable representations for a fixed $d$ with a computer algebra system such as the GAP package QPA?
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Finding all $d$-dimensional indecomposable representations
Now this is implemented in QPA version 1. There is an error above, one needs to consider both `ExtOverAlgebra(S[i],iso[j])` and `ExtOverAlgebra(iso[j],S[i])` in order to get all modules of the given length. It looks like this in QPA:



```
gap> A := KroneckerAlgebra(GF(3),2);; 
gap> AllModulesOfLengthAtMost( A, 4 );     
[ <[ 0, 0 ]>, <[ 1, 0 ]>, <[ 0, 1 ]>, <[ 1, 1 ]>, <[ 1, 1 ]>, <[ 1, 1 ]>, 
  <[ 1, 1 ]>, <[ 1, 1 ]>, <[ 2, 1 ]>, <[ 2, 1 ]>, <[ 2, 1 ]>, <[ 2, 1 ]>, 
  <[ 2, 1 ]>, <[ 2, 1 ]>, <[ 1, 2 ]>, <[ 1, 2 ]>, <[ 1, 2 ]>, <[ 1, 2 ]>, 
  <[ 1, 2 ]>, <[ 1, 2 ]>, <[ 3, 1 ]>, <[ 3, 1 ]>, <[ 3, 1 ]>, <[ 3, 1 ]>, 
  <[ 3, 1 ]>, <[ 2, 2 ]>, <[ 3, 1 ]>, <[ 2, 2 ]>, <[ 2, 2 ]>, <[ 2, 2 ]>, 
  <[ 2, 2 ]>, <[ 2, 2 ]>, <[ 2, 2 ]>, <[ 2, 2 ]>, <[ 2, 2 ]>, <[ 2, 2 ]>, 
  <[ 2, 2 ]>, <[ 2, 2 ]>, <[ 2, 2 ]>, <[ 2, 2 ]>, <[ 2, 2 ]>, <[ 2, 2 ]>, 
  <[ 2, 2 ]>, <[ 2, 2 ]>, <[ 2, 2 ]>, <[ 2, 2 ]>, <[ 2, 2 ]>, <[ 2, 2 ]>, 
  <[ 2, 2 ]>, <[ 2, 2 ]>, <[ 1, 3 ]>, <[ 1, 3 ]>, <[ 1, 3 ]>, <[ 1, 3 ]>, 
  <[ 1, 3 ]>, <[ 1, 3 ]> ]
gap> AllIndecModulesOfLengthAtMost( A, 4 );
[ <[ 1, 0 ]>, <[ 0, 1 ]>, <[ 1, 1 ]>, <[ 1, 1 ]>, <[ 1, 1 ]>, <[ 1, 1 ]>, 
  <[ 2, 1 ]>, <[ 1, 2 ]>, <[ 2, 2 ]>, <[ 2, 2 ]>, <[ 2, 2 ]>, <[ 2, 2 ]>, 
  <[ 2, 2 ]>, <[ 2, 2 ]>, <[ 2, 2 ]> ]

```

The first one finds all non-isomorphic modules of length at most 4, and the second one finds all non-isomorphic indecomposable modules of length at most 4.


I hope that these comments are helpful.


Best regards, the QPA-team.


