# Stable equivalence and stable Auslander algebras

Let $$A$$ be a representation-finite finite dimensional quiver algebra and $$M$$ the basic direct sum of all indecomposable $$A$$-modules. Recall that the Auslander algebra of $$A$$ is $$End_A(M)$$ and the stable Auslander algebra of $$A$$ is the stable endomorphism ring of $$M$$.

Questions:

Is the stable Auslander algebra of $$A$$ the quiver algebra having the stable Auslander-Reiten quiver with mesh relations (that is obtained from the usual Auslander algebra by deleting all projective vertices and related vertices)?

Are two algebras $$A_1$$ and $$A_2$$ stable equivalent if and only if their stable Auslander algebras are isomorphic as algebras?

Is there a computational way using QPA to check whether two (representation-finite)algebras $$A$$ and $$B$$ are stable equivalent?

It might be that one has to assume that the involved algebras are standard since there are counterexamples for the corresponding results about Auslander algebras for non-standard examples. But I am not sure about the stable version and surprisingly I have not found results about this in the literature.