Stable Auslander–Reiten quiver (${\Gamma }_s(A)$)

For a self-injective finite-dimensional algebra, remove the projective vertices from its Auslander–Reiten quiver. The resulting stable quiver has vertices the nonprojective indecomposable modules. Its translation sends the end term of an almost-split exact sequence to its start term. In particular a quiver of shape $\mathbb{Z}{A}_s/⟨{\tau }^e⟩$ has $es$ vertices.