{
  "abstract": "We prove that every Igusa--Todorov Artin algebra satisfies the Auslander--Reiten conjecture. More precisely, let $V$ be an $n$-Igusa--Todorov witness, and let $t$ be the number of isomorphism classes of nonprojective indecomposable summands of $V$. If a finitely generated module $M$ satisfies $\\Ext_A^i(M,A)=0$ for every $i>0$ and $\\Ext_A^q(M,M)=0$ for $1\\leq q\\leq 2t+1$, then $M$ is projective. As applications, algebras of representation dimension at most three and algebras satisfying $J^{2m+1}=0$ for which $A/J^m$ has finite representation type satisfy the Auslander--Reiten conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14453",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiaojin Zhang"
    },
    {
      "name": "Panyue Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3s83n8ynxshj7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14453",
  "fulltext_url": null,
  "id": "3s83n8ynxshj7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14453",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7213424074",
  "pdf_url": "https://arxiv.org/pdf/2609.14453",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3s83n8ynxshj7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.14453",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14453"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Igusa--Todorov Algebras and the Auslander--Reiten Conjecture",
  "title_text": "Igusa--Todorov Algebras and the Auslander--Reiten Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/3s83n8ynxshj7",
  "venue": "arXiv",
  "versions": []
}