c-vectors and dimension vectors for cluster-finite quivers (Q2865920)

The main result of this note is the observation that a positive \(\mathbf{c}\)-vector associated with a quiver equipped with a non-degenerate potential equals the dimension vector of a certain module for the corresponding Jacobian algebra. As a consequence, it follows that for quivers which are mutation equivalent to a Dynkin quiver the set of positive \(\mathbf{c}\)-vectors equals the set of dimension vectors for indecomposable modules over the corresponding Jacobian algebra. Several examples are provided.