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$ .
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.