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Minimal algebras of infinite representation type with preprojective component

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Abstract

Let A be a finite dimensional, basic and connected algebra (associative, with 1) over an algebraically closed field k. Denote by e1,...,en a complete set of primitive orthogonal idempotents in A and by Ai= A/AeiA. A is called a minimal algebra of infinite representation type provided A is itself of infinite representation type,whereas all Ai, 1≤i≤n,are of finite representation type. The main result gives the classification of the minimal algebras having a preprojective component in their Auslander-Reiten quiver. The classification is obtained by realizing that these algebras are essentially given by preprojective tilting modules over tame hereditary algebras.

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  1. Fakultät für Mathematik Universität Bielefeld, D 4800, Bielefeld 1, BR Deutschland

    Dieter Happel & Dieter Vossieck

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  1. Dieter Happel
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  2. Dieter Vossieck
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Happel, D., Vossieck, D. Minimal algebras of infinite representation type with preprojective component. Manuscripta Math 42, 221–243 (1983). https://doi.org/10.1007/BF01169585

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  • DOI: https://doi.org/10.1007/BF01169585

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