{
  "abstract": "In this work, we complete the description of the one-dimensional partial actions of 8-dimensional Hopf algebras by computing the remaining cases: the Kac-Paljutkin algebra $\\mathcal{A}$ and the unique non-semisimple non-pointed Hopf algebra $\\mathcal{K}$. We prove that all these partial actions are symmetric, study their associated partial smash products and we determine all their partial coactions of dimension one. Beyond the 8-dimensional setting, we investigate which right coideal subalgebras of a Hopf algebra $H$ can be realized as partial smash products $\\underline{ \\Bbbk \\# H}$ over the base field. In particular, we show that every right coideal subalgebra of a finite-dimensional cosemisimple Hopf algebra arises in this way.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13502",
  "author_total": 4,
  "authors": [
    {
      "name": "Matheus Castelo"
    },
    {
      "name": "Leonardo Duarte Silva"
    },
    {
      "name": "William Hautekiet"
    },
    {
      "name": "Grasiela Martini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/35fp709m0tmw1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13502",
  "fulltext_url": null,
  "id": "35fp709m0tmw1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13502",
  "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.QA"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7213308567",
  "pdf_url": "https://arxiv.org/pdf/2609.13502",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/35fp709m0tmw1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.13502",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13502"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "One-dimensional partial actions of 8-dimensional Hopf algebras and right coideal subalgebras",
  "title_text": "One-dimensional partial actions of 8-dimensional Hopf algebras and right coideal subalgebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/35fp709m0tmw1",
  "venue": "arXiv",
  "versions": []
}