Selfinjective algebras having a generalized standard family of quasi-tubes maximally saturated by simple and projective modules

TL;DR

This paper classifies certain selfinjective algebras based on their Auslander-Reiten quiver structure, identifying them as algebras of strictly canonical type with specific quasi-tube families.

Contribution

It provides a complete characterization of selfinjective algebras with a generalized standard family of quasi-tubes maximally saturated by simple and projective modules.

Findings

Algebras are of strictly canonical type.

Characterization of the Auslander-Reiten quiver structure.

Complete description of the algebra class.

Abstract

We give a complete description of finite dimensional selfinjective algebras over an algebraically closed field whose Auslander-Reiten quiver admits a generalized standard family of quasi-tubes maximally saturated by simple and projective modules. In particular, we show that these algebras are selfinjective algebras of strictly canonical type.