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Research Article | Open Access

Homological conjectures and stable equivalences of Morita type

Juxiang Sun1( ), Guoqiang Zhao2
School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu 476000, China
School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
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Abstract

Let A and B be two finite-dimensional algebras over an algebraically closed field. Suppose that A and B are stably equivalent of Morita type; we prove that A satisfies the Auslander–Reiten conjecture (resp. Gorenstein projective conjecture, strong Nakayama conjecture, Auslander–Gorenstein conjecture, Nakayama conjecture, Gorenstein symmetric conjecture) if and only if B does so. This can provide new classes of algebras satisfying homological conjectures, and we give an example to illustrate it.

Keywords

Auslander–Reiten conjectureGorenstein projective conjecturestrong Nakayama conjecturegeneralized Nakayama conjecturestable equivalence of Morita typeGorenstein projective module
CLC number: 16E10, 16E30

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AIMS Mathematics
Volume 10 Issue 2,
February 2025
Pages 2589-2601
DOI: 10.3934/math.2025120

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Cite this article:
Sun J, Zhao G. Homological conjectures and stable equivalences of Morita type. AIMS Mathematics, 2025, 10(2): 2589-2601. https://doi.org/10.3934/math.2025120

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Received: 12 December 2024
Revised: 16 January 2025
Accepted: 23 January 2025
Published: 15 February 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)