manuscripta mathematica

, Volume 46, Issue 1–3, pp 117–136 | Cite as

Critical simply connected algebras

  • Klaus Bongartz


It is well-known that simply connected algebras are uniquely determined by a graded tree.Reversely,each graded tree gives rise to a not necessarily representation-finite algebra. We call an algebra critical provided it is not representation-finite, but any proper convex full subalgebra is.All critical algebras arising from graded trees are classified.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    BAUTISTA,R.,BRENNER,S.:On the number of terms in the middle of an almost split sequence,Proc. of ICRA III,Puebla 1980,LNM 903,pp.1–9Google Scholar
  2. 2.
    BONGARTZ,K.: Treue einfach zusammenhängende Algebren I, Comment.Math.Helv. 57 (1982),282–330Google Scholar
  3. 3.
    BONGARTZ,K.: Algebras and quadratic forms,to appear in JLMSGoogle Scholar
  4. 4.
    BONGARTZ,K.:Ein Kriterium für endlichen Darstellungstyp,preprint January 1983,22 pagesGoogle Scholar
  5. 5.
    BONGARTZ,K.,GABRIEL,P.:Covering spaces in representation theory, Invent.math. 65 (1982),331–378Google Scholar
  6. 6.
    BRETSCHER,O.,GABRIEL,P.:The standard form of a representation-finite algebra, Bull.Soc.math.France, 111 (1983),pp.21–40Google Scholar
  7. 7.
    DLAB,V.,RINGEL,C.M.: Indecomposable representations of graphs and algebras,Memoirs Amer.Math.Soc. 173 (1976)Google Scholar
  8. 8.
    HAPPEL,D.,VOSSIECK,D.:Minimal algebras of infinite representation type with preprojective component, Man.math.,Vol.42 (1983),221–243Google Scholar
  9. 9.
    KLEINER,M.M.: Partially ordered sets of finite type, Zap.Naucn.Sem. LOMI 28 (1972), 32–41Google Scholar
  10. 10.
    NAZAROVA,L.A.,ROITER,A.V.:Representations of partially ordered sets,Zap.Naucn.Sem. LOMI 28 (1972)Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Klaus Bongartz
    • 1
  1. 1.Math.Institut BUniversität Stuttgart7 Stuttgart 1

Personalised recommendations