{
  "abstract": "Under suitable group actions, it is known that $A_\\infty$-structures descend to orbit categories. We study the converse problem of lifting an $A_\\infty$-structure to a prescribed covering. We show that a compatible group grading determines a canonical lift, uniquely characterized by the strictness of the covering projection. As an application, we construct $A_\\infty$-categories associated with admissible fractional Brauer graph algebras by lifting Brauer graph $A_\\infty$-categories. Their geometric data augment the surface models of Brauer graph algebras with a Nakayama character encoding the covering. We prove that admissible fractional Brauer graph algebras with equivalent geometric data are derived equivalent. Furthermore, we establish a set of combinatorial derived invariants and prove their completeness in reduced genus zero and in reduced genus at least two when the defining ribbon graph is non-bipartite.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27660",
  "author_total": 1,
  "authors": [
    {
      "name": "Bohan Xing"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/evg72bjxe9106.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27660",
  "fulltext_url": null,
  "id": "evg72bjxe9106",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27660",
  "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.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7214238150",
  "pdf_url": "https://arxiv.org/pdf/2609.27660",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/evg72bjxe9106.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27660",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27660"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Lifting $A_\\infty$-structures through coverings with applications to fractional Brauer graph algebras",
  "title_text": "Lifting A_∞-structures through coverings with applications to fractional Brauer graph algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/evg72bjxe9106",
  "venue": "arXiv",
  "versions": []
}