# Classification of representation-finite algebras up to stable equivalence of Morita type

Assume $K$ is an algebraically closed field.

I wanted to ask if there is a classification of the representation-finite $K$-algebras up to stable equivalence of Morita type (at least for some small numbers of simple modules).

Fischbacher classified all representation-finite algebras up to Morita equivalence with at most 3 simple modules, and there is a paper listing them by quiver and relations.

This list seems very complicated (it contains about 40 quivers with many possible choices of relations), and perhaps it could get much smaller if one tries to classify them up to stable equivalence of Morita type.

To give a precise question, let me start like this:

Is there a list of quivers and relations classifying all representation-finite algebras with at most 3 simple modules up to stable equivalence of Morita type (or maybe derived equivalence, stable equivalence, etc.)?

If no, is there such a list if we additionally assume the algebras to be self-injective?

In the latter case, I know that the classification is known but I could not find a list with quivers and relations for such self-injective representation-finite algebras with at most 3 simple modules.