{
  "abstract": "We prove a multiplication formula for the Wang-Wei-Zhang cluster character on a Hom-finite $2$-Calabi--Yau Frobenius extriangulated category $\\mathcal C$ with a cluster-tilting object under the assumption that its stable category has constructible cones with respect to the induced cluster-tilting object. This formula generalizes those obtained by Wang-Wei-Zhang for $\\mathcal C$ in the one-dimensional case and by Keller-Plamondon-Qin for (stably) $2$-Calabi-Yau Frobenius or triangulated categories. As a consequence, we express the frozen term in an Auslander-Reiten mesh with the character of a minimal cosyzygy middle term. For acyclic quivers with principal coefficients, we compute these frozen multiplicities in Higgs categories and obtain explicit principal coefficient mesh relations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20049",
  "author_total": 3,
  "authors": [
    {
      "name": "Ming Ding"
    },
    {
      "name": "Fan Xu"
    },
    {
      "name": "Panyue Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eyqrebmjztgb9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20049",
  "fulltext_url": null,
  "id": "eyqrebmjztgb9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20049",
  "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.CT"
    ],
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.20049",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eyqrebmjztgb9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20049",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20049"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A refined multiplication formula in 2-Calabi-Yau Frobenius extriangulated categories",
  "title_text": "A refined multiplication formula in 2-Calabi-Yau Frobenius extriangulated categories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/eyqrebmjztgb9",
  "venue": "arXiv",
  "versions": []
}