A characterization of selfinjective algebras of strictly canonical type

We prove that the class of selfinjective algebras of strictly canonical type, investigated in Kwiecień and Skowroński (2009) [27], Kwiecień and Skowroński (2009) [28], coincides with the class of selfinjective algebras having triangular Galois coverings with infinite cyclic group and the Auslander–Reiten quiver with quasi-tubes maximally saturated by simple and projective modules, satisfying natural conditions.