manuscripta mathematica

, Volume 42, Issue 2, pp 221–243

Minimal algebras of infinite representation type with preprojective component

Authors

  • Dieter Happel
    • Fakultät für Mathematik Universität Bielefeld
  • Dieter Vossieck
    • Fakultät für Mathematik Universität Bielefeld
Article

DOI: 10.1007/BF01169585

Cite this article as:
Happel, D. & Vossieck, D. Manuscripta Math (1983) 42: 221. doi:10.1007/BF01169585

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.

Copyright information

© Springer-Verlag 1983