Ext-finite modules for weakly symmetric algebras with radical cube zero

TL;DR

This paper classifies weakly symmetric indecomposable algebras with radical cube zero, showing that those of wild representation type lack non-projective modules with finite-dimensional ext algebras, thus providing a complete classification.

Contribution

It provides a complete classification of weakly symmetric indecomposable algebras with radical cube zero regarding the existence of non-projective modules with finite-dimensional ext algebras.

Findings

Wild type algebras lack such modules

Complete classification of relevant algebras

Characterization of modules based on ext algebra finiteness

Abstract

Assume $A$ is weakly symmetric, indecomposable, with radical cube zero and radical square non-zero. We show that such algebra of wild representation type does not have a non-projective module $M$ whose ext algebra is finite-dimensional. This gives a complete classification weakly symmetric indecomposable algebras which have a non-projective module whose ext algebra is finite-dimensional.