Embedding of the vertices of the Auslander–Reiten quiver of an iterated tilted algebra of Dynkin type Δ in [formula omitted

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 A ̂ its repetitive algebra. We approach the problem of finding a combinatorial algorithm giving the embedding of the vertices of the Auslander–Reiten quiver Γ A of A in the Auslander–Reiten quiver Γ( mod ( A ̂ ))≃ ZΔ of the stable category mod ( A ̂ ) . 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 Γ A in ZΔ for any algebra A such that T( A)≃ T.