Abstract
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.
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References
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.1–9
BONGARTZ,K.: Treue einfach zusammenhängende Algebren I, Comment.Math.Helv. 57 (1982),282–330
BONGARTZ,K.: Algebras and quadratic forms,to appear in JLMS
BONGARTZ,K.:Ein Kriterium für endlichen Darstellungstyp,preprint January 1983,22 pages
BONGARTZ,K.,GABRIEL,P.:Covering spaces in representation theory, Invent.math. 65 (1982),331–378
BRETSCHER,O.,GABRIEL,P.:The standard form of a representation-finite algebra, Bull.Soc.math.France, 111 (1983),pp.21–40
DLAB,V.,RINGEL,C.M.: Indecomposable representations of graphs and algebras,Memoirs Amer.Math.Soc. 173 (1976)
HAPPEL,D.,VOSSIECK,D.:Minimal algebras of infinite representation type with preprojective component, Man.math.,Vol.42 (1983),221–243
KLEINER,M.M.: Partially ordered sets of finite type, Zap.Naucn.Sem. LOMI 28 (1972), 32–41
NAZAROVA,L.A.,ROITER,A.V.:Representations of partially ordered sets,Zap.Naucn.Sem. LOMI 28 (1972)
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Bongartz, K. Critical simply connected algebras. Manuscripta Math 46, 117–136 (1984). https://doi.org/10.1007/BF01185198
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DOI: https://doi.org/10.1007/BF01185198