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

Let Delta be a Dynkin diagram and k an algebraically closed field. Let A be an iterated tilted finite-dimensional k-algebra of type A 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 Gamma(A) of A in the Auslander-Reiten quiver Gamma((mod) under bar((A) over cap)) similar or equal to ZDelta of the stable category (mod) under bar((A) over cap). Let T be a trivial extension of finite representation type and Car-tan class A. Assume that we know the vertices of ZDelta corresponding to the radicals of the indecomposable projective T-modules. We determine the embedding of Gamma(A) in ZDelta for any algebra A such that T(A) similar or equal to T. (C) 2003 Elsevier Science (USA). All rights reserved.