Let $A=KQ$ be a path algebra of a connected quiver. (K algebraically closed if it helps)
Question: Is there an explicit classification of all indecomposable $A$-modules $M$ that are rigid, that is $Ext_A^1(M,M)=0$?
Some comments:
-Note that being rigid implies that $End_A(M) \cong K$ and thus it feels like that there are not too many.
-All preprojective/preinjective indeocomposable modules are rigid and thus we can assume that $M$ is regular.
-If $Q$ is of Euclidean type, there are only finitely many such $M$ that are regular. Is there a quick way to obtain those regular rigid $M$ in the Euclidean case using the GAP-package QPA?
