{
  "abstract": "We show that Jacobi-finite potentials need not exist on finite $2$-acyclic quivers. Our main tool is a matrix-valued Golod--Shafarevich--Vinberg inequality for quotients of completed path algebras by finitely many, possibly nonhomogeneous, topological relations. Applied to cyclic derivatives, it yields a potential-dependent obstruction to the finite-dimensionality of completed Jacobian algebras. We then construct a purely quiver-level criterion excluding every Jacobi-finite potential on a given quiver, and exhibit a family of quivers for which every potential has an infinite-dimensional Jacobian algebra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11200",
  "author_total": 2,
  "authors": [
    {
      "name": "Wen Chang"
    },
    {
      "name": "QuanYu Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3zwgjt4g7a3ax.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11200",
  "fulltext_url": null,
  "id": "3zwgjt4g7a3ax",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11200",
  "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.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7212302913",
  "pdf_url": "https://arxiv.org/pdf/2609.11200",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3zwgjt4g7a3ax.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11200",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11200"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Obstructions to Jacobi-Finiteness of Quivers with Potentials",
  "title_text": "Obstructions to Jacobi-Finiteness of Quivers with Potentials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/3zwgjt4g7a3ax",
  "venue": "arXiv",
  "versions": []
}