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 and some additional relations (what are those additional relations? Probably the mesh relations where the deleted arrows are set to zero)?
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?