{
  "abstract": "In this paper, we show that for any coquasi-Hopf algebra $H$ and any $H$-Majid bimodule $M$, the cotensor coalgebra $\\operatorname{CoT}_H(M)$ admits a graded coquasi-Hopf algebra structure. We then define the standard filtration of a coquasi-Hopf algebra and show that the associated graded coquasi-Hopf algebra admits an embedding into a cotensor coquasi-Hopf algebra that preserves degrees zero and one. If, in addition, this coquasi-Hopf algebra is coquasitriangular (respectively, coribbon), then the cotensor coquasi-Hopf algebra is also coquasitriangular (respectively, coribbon), and the above embedding is a morphism of coquasitriangular (respectively, coribbon) coquasi-Hopf algebras. As a byproduct, we prove that the coquasi-antipode of a coquasi-Hopf algebra with the dual Chevalley property is bijective. Moreover, we establish graded quasi-coquasi-Hopf pairings between tensor quasi-Hopf algebras and cotensor coquasi-Hopf algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08361",
  "author_total": 2,
  "authors": [
    {
      "name": "Jing Yu"
    },
    {
      "name": "Xiangjun Zhen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c132bcb61zry2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08361",
  "fulltext_url": null,
  "id": "c132bcb61zry2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08361",
  "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.QA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7220920556",
  "pdf_url": "https://arxiv.org/pdf/2610.08361",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c132bcb61zry2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.08361",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08361"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Quasi-quantum groups arising from cotensor coquasi-Hopf algebras",
  "title_text": "Quasi-quantum groups arising from cotensor coquasi-Hopf algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/c132bcb61zry2",
  "venue": "arXiv",
  "versions": []
}