Abstract. We develop the representation theory of selfinjective algebras of strictly canonical type and prove that their Auslander-Reiten quivers admit quasi-tubes maximally saturated by simple and projective modules.
Abstract. In continuation of our article in Colloq. Math. 116.1, we give a complete description of the symmetric algebras of strictly canonical type by quivers and relations, using Brauer quivers.
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.
We give necessary and sufficient conditions for a wing of an Auslander-Reiten quiver of a selfinjective algebra to be the wing of the radical of an indecomposable projective module. Moreover, a characterization of indecomposable Nakayama algebras of Loewy length ≥ 3 is obtained.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.