Higher torsion-free Auslander-Reiten sequences and the dominant dimension of algebras

Published 2 Apr 2024 in math.RT and math.RA | (2404.02274v1)

Abstract: We generalise a theorem of Tachikawa about reflexive Auslander-Reiten sequences. We apply this to give a new characterisation of the dominant dimension of gendo-symmetric algebras. We also generalise a formula due to Reiten about the dominant dimension of an algebra $A$ and grades of torsion $A$-modules.

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