I have the following question(s):
I have an "Algebra-With-One" $R$ as a subalgebra of a full matrix algebra in GAP.
Furthermore, I have 5 primitive orthogonal idempotents $e_1,...,e_5$, which sum up to $1_R$ (the identity matrix).
I would like to compute the projective indecomposable modules $P_1=e_1R,...,P_5=e_5R$ with GAP (or another computer programm (e.g. SAGE) which can handle with algebras and modules and maybe even the GAP data (e.g. the algebra R) I have produced so far)
and then I would like to test, whether $P_i$ and $P_j$ are isomorphic as $R$-modules for $i\neq j$.
I also would like to compute the algebras $e_i R e_j$ for all $i$ and $j$.
I can access the generators (as matrices) of the algebra $R$ and I know $e_i=...$ (as matrices).
Is GAP or any other freely available computer program able to calculate with these things (projective R-modules, etc.)?
Thank you very much.