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Degenerations for modules over representation-finite selfinjective algebras. (English) Zbl 1054.16502

From the text: This is a continuation of the author’s earlier paper [J. Algebra 198, No. 2, 563–581 (1997; Zbl 0902.16015)]. Here the author investigates representation-finite self-injective algebras. The main result shows that for these algebras the partial orders \(\leq_{\text{ext}}\) and \(\leq_{\text{eg}}\) are different if and only if the stable Auslander-Reiten quiver \(\Gamma^s(A)\) of \(A\) is of the form \(\mathbb{Z} D_{3m}/(\tau^{2m-1})\) for some \(m\geq 2\).

MSC:

16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
16G60 Representation type (finite, tame, wild, etc.) of associative algebras
16G20 Representations of quivers and partially ordered sets

Citations:

Zbl 0902.16015
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