Embedding of the vertices of the Auslander-Reiten quiver of an iterated tilted algebra of Dynkin type Δ in ZΔ

Abstract

Let Δ be a Dynkin diagram and k an algebraically closed field. Let A be an iterated tilted finite-dimensional k-algebra of type Δ and denote by  its repetitive algebra. We approach the problem of finding a combinatorial algorithm giving the embedding of the vertices of the Auslander-Reiten quiver ΓA of A in the Auslander-Reiten quiver Γ(mod(Â)) ≃ ℤΔ of the stable category mod(Â). Let T be a trivial extension of finite representation type and Cartan class Δ. Assume that we know the vertices of ℤΔ corresponding to the radicals of the indecomposable projective T-modules. We determine the embedding of ΓA in ℤΔ for any algebra A such that T(A) ≃ T.