Exceptional modules are tree modules Original Research Article

We consider representations of a quiver over an arbitrary field. Recall that an indecomposable representation M without self-extensions is said to be exceptional. We are going to show that exceptional representations can be exhibited using matrices involving as coefficients just 0 and 1. Actually, if d is the dimension of M, there exists such a matrix presentation with precisely d − 1 non-zero coefficients: the corresponding “coefficient quiver” is a tree.