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Maximal n-orthogonal modules for selfinjective algebras

by Karin Erdmann, Thorsten Holm.

Series: 2006-19, Preprints

16G10 Representations of Artinian rings
16D50 Injective modules, self-injective rings
16E10 Homological dimension
16G70 ~Auslander-Reiten sequences (almost split sequences) and ~Auslander-Reiten quivers

Let A be a selfinjective algebra.
We show that, for any n, maximal n-orthogonal
A-modules (in the sense of Iyama) rarely exist.
More precisely, we prove that if A admits a
maximal n-orthogonal module, then all A-modules
are of complexity at most 1.

Selfinjective algebras; Maximal n-orthogonal modules