Abstract
In this paper, we present a new approach to the problem of classifying all basic finite-dimensional algebras over an algebraically closed field k which are connected, selfinjective and representation-finite. By [12], we can associate with such an algebra λ a Dynkin-graph λ, a subset C of vertices of ℤΔ (see fig.1) and a non-trivial automorphism group II of ℤΔ stabilizing C, in such a way that these data uniquely determine the Auslander-Reiten quiver of λ. Our main result is an alternate description of these sets C.
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