Realizations of Frobenius Functions

In an earlier paper (Ágoston et al.,CMS Conf. Proc.18(1996), 17–37) we studied the so-called Frobenius functions on certain translation quivers. Here we show that the classification given there is in some sense complete: every Frobenius length function on the wingW(n) and the tubeT(n) is equivalent to the length function on a convex subquiver of the Auslander–Reiten quiver of the module category over some algebraA.