manuscripta mathematica

, Volume 42, Issue 2, pp 221-243

First online:

Minimal algebras of infinite representation type with preprojective component

  • Dieter HappelAffiliated withFakultät für Mathematik Universität Bielefeld
  • , Dieter VossieckAffiliated withFakultät für Mathematik Universität Bielefeld

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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.