{
  "abstract": "Let $B$ and $D$ be both algebras and coalgebras in a braided monoidal category $\\mathcal{C}$. In the literature, there are equivalent conditions for $(B,D)$ to form a generalized smash biproduct (or cross product) denoted by $B\\times D$, which were mainly given by Bespalov and Drabant in 1999 as well as by Bulacu, Caenepeel and Torrecillas in 2013. This paper is devoted to constructing another biproduct $D\\times B^\\ast$ when $B$ has a left dual object $B^\\ast$ in $\\mathcal{C}$. As results, we show that $B\\times D$ is left smash over $D\\times B^\\ast$, and establish a specific isomorphism ${}_{B\\times D}\\mathfrak{YD}(\\mathcal{C})^{B\\times D}\\cong{}_{D\\times B^\\ast}\\mathfrak{YD}(\\mathcal{C})^{D\\times B^\\ast}$ between the categories of the (left-right) Yetter-Drinfeld modules in $\\mathcal{C}$. The constructions and results are provided in three levels: (1) $B\\times D$ is an algebra and a coalgebra; (2) $B\\times D$ is a bialgebra; (3) $B\\times D$ is a Hopf algebra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39896",
  "author_total": 1,
  "authors": [
    {
      "name": "Kangqiao Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/59wd2eh0hesca.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39896",
  "fulltext_url": null,
  "id": "59wd2eh0hesca",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39896",
  "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.CT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7215039192",
  "pdf_url": "https://arxiv.org/pdf/2609.39896",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/59wd2eh0hesca.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39896",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39896"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Characterization Results on Generalized Smash Biproduct Hopf Algebras over the Partial Dual Construction",
  "title_text": "Characterization Results on Generalized Smash Biproduct Hopf Algebras over the Partial Dual Construction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/59wd2eh0hesca",
  "venue": "arXiv",
  "versions": []
}