The \(N=1\) quivers of types \(A_n\) and \(D_n\) have finite representation type. (Q2469519)

In the paper \(N=1\) \(\Delta\) quivers are investigated (for \(\Delta=\mathbb{A}_n,\mathbb{D}_n\)). The \(N=1\) \(\Delta\) quiver is constructed from the quiver \(\Delta\) by adding a loop to any vertex, replacing each edge of \(\Delta\) by a pair of opposite directed edges and adding certain relations. In the paper the author gives conditions which are sufficient to decide that an \(N=1\) \(\mathbb{A}_n\) (resp. \(N=1\) \(\mathbb{D}_n\)) quiver is of finite representation type (i.e. there exist only finitely many isomorphism classes of indecomposable representations of this quiver).