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Hi, I have the following question:

Given a $\mathbb{Q}$-algebra A by generators (the generators are matrices) and knowing 5 primitive orthogonal idempotents $e_1$,...,$e_5$ (as matrices), which sum up to $1_R$ (the identity matrix), is there a way / procedure in SAGE, that can compute the projective indecomposable modules $P_1=e_1\cdot R$,...,$P_5=e_5\cdot R$ and then test, whether $P_i$ and $P_j$ are isomorphic as $R$-modules for $i\neq j$?

Thank you very much.

Hi, I have the following question:

Given a $\mathbb{Q}$-algebra A by generators (the generators are matrices) and knowing 5 primitive orthogonal idempotents $e_1$,...,$e_5$ (as matrices), which sum up to $1_R$ $1_A$ (the identity matrix), is there a way / procedure in SAGE, that can compute the projective indecomposable modules $P_1=e_1\cdot R$,...,$P_5=e_5\cdot R$ A$,...,$P_5=e_5\cdot A$ and then test, whether $P_i$ and $P_j$ are isomorphic as $R$-modules $A$-modules for $i\neq j$?

Thank you very much.