English

On weakly Gorenstein algebras

Representation Theory 2023-10-30 v2

Abstract

We prove that algebras are left weakly Gorenstein in case the subcategory AΩn(A)^{\perp}A \cap \Omega^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.

Keywords

Cite

@article{arxiv.1908.04738,
  title  = {On weakly Gorenstein algebras},
  author = {Rene Marczinzik},
  journal= {arXiv preprint arXiv:1908.04738},
  year   = {2023}
}

Comments

The results of this article are now included in arXiv:1608.04212

R2 v1 2026-06-23T10:46:33.038Z