On weakly Gorenstein algebras

Published: August 13, 2019Updated: October 27, 2023PDF arXiv

Abstract

We prove that algebras are left weakly Gorenstein in case the subcategory $^{\perp}A \cap Ω^n(A)$ is representation-finite. This applies in particular to all monomial algebras and endomorphism algebras of modules over representation-finite algebras. We also give a proof of the Auslander-Reiten conjecture for such algebras.

On weakly Gorenstein algebras

Rene Marczinzik

math.RT

Published: August 13, 2019Updated: October 27, 2023PDF arXiv

Abstract

We prove that algebras are left weakly Gorenstein in case the subcategory $^{\perp}A \cap Ω^n(A)$ is representation-finite. This applies in particular to all monomial algebras and endomorphism algebras of modules over representation-finite algebras. We also give a proof of the Auslander-Reiten conjecture for such algebras.