{
  "abstract": "Let $d \\geqslant 1$ be an integer, $\\mathscr{M}$ a suitable $d$-abelian category. There is a notion of higher torsion classes in $\\mathscr{M}$, also known as $d$-torsion classes. We generalise a classic theorem of Hoshino by providing criteria for a $d$-torsion class $\\mathscr{U}$ to be splitting, notably that $\\mathscr{U}$ is stable under $τ_d^-$, the inverse $d$-Auslander--Reiten translation. We apply the criteria to show that under additional assumptions, which are satisfied in Dynkin type $A$, the elements of the spine of the lattice of $d$-torsion classes are precisely the splitting $d$-torsion classes. The spine consists of the elements which belong to a chain of maximal length.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07953",
  "author_total": 3,
  "authors": [
    {
      "name": "Erlend D. Børve"
    },
    {
      "name": "Peter Jorgensen"
    },
    {
      "name": "Mads Hustad Sandøy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cjsyrnt055rnq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07953",
  "fulltext_url": null,
  "id": "cjsyrnt055rnq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07953",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7212081385",
  "pdf_url": "https://arxiv.org/pdf/2609.07953",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cjsyrnt055rnq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07953",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07953"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Splitting torsion classes in higher homological algebra",
  "title_text": "Splitting torsion classes in higher homological algebra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/cjsyrnt055rnq",
  "venue": "arXiv",
  "versions": []
}