06-19
Maximal n-orthogonal modules for selfinjective algebras
by Karin Erdmann; Thorsten Holm
Preprint series: 06-19, Preprints
- MSC:
- 16G10 Representations of Artinian rings
- 16D50 Injective modules, self-injective rings, See also {16L60, 18G05}
- 16E10 Homological dimension
- 16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
Abstract: 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.
Keywords: Selfinjective algebras; Maximal n-orthogonal modules
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