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Selfinjective and simply connected algebras

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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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  1. Mathematisches Institut, Universität Zurich, Freiestrasse 36, CH-8032, Zürich, Switzerland

    Otto Bretscher, Christian Läser & Christine Riedtmann

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  1. Otto Bretscher
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  2. Christian Läser
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  3. Christine Riedtmann
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Bretscher, O., Läser, C. & Riedtmann, C. Selfinjective and simply connected algebras. Manuscripta Math 36, 253–307 (1981). https://doi.org/10.1007/BF01322494

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