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On homogeneous exact categories. (English) Zbl 0962.16012

Die Hauptergebnisse des Artikels sind die folgenden zwei Sätze: Es sei \(\Lambda\) eine endlich dimensionale Algebra über einem Körper \(k\). Sei \(\mathcal C\) die Kategorie der Linksmodule über der Polynomalgebra \(\Lambda[t]\) in einer Variablen \(t\), die endlich dimensional und als Linksmodule über \(\Lambda\) auch projektiv sind. Satz 1: Ist \(\Lambda\) selbst-injektiv, so hat \(\mathcal C\) fast zerfallende Sequenzen. Satz 2: Ist \(\Lambda\) symmetrisch, so ist \(\mathcal C\) stark homogen, das heißt \(\mathcal C\) hat fast zerfallende Sequenzen und weder projektive Objekte noch injektive Objekte, und jedes unzerlegbare Objekt in \(\mathcal C\) ist homogen.

MSC:

16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
16G60 Representation type (finite, tame, wild, etc.) of associative algebras
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