{
  "abstract": "In this paper, we investigate higher-order symmetries and non-geometric symmetries within the framework of $k$-cosymplectic Hamiltonian field theory. We introduce the concept of generalized infinitesimal symmetry, which relaxes the standard symmetry condition, and then define two new classes of symmetries: higher-order general infinitesimal Cartan symmetries and good non-geometric symmetries. For each of these symmetry classes, we establish a Noether-type theorem that provides explicit conserved quantities for exact $k$-cosymplectic Hamiltonian systems. These results extend and generalize previous work on standard Cartan symmetries in the $k$-cosymplectic setting. Furthermore, we extend all of these results in a parallel fashion to Hamiltonian systems on $k$-symplectic manifolds, demonstrating the unifying nature of our approach. Concrete examples are provided to illustrate the existence and applicability of the proposed symmetries. Our framework offers a systematic geometric treatment of generalized symmetries and their associated conservation laws in classical field theories.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23034",
  "author_total": 2,
  "authors": [
    {
      "name": "Manuel de León"
    },
    {
      "name": "Xuefeng Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ehc8dxdh8mj40.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23034",
  "fulltext_url": null,
  "id": "ehc8dxdh8mj40",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23034",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
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  "openalex": "W7214006887",
  "pdf_url": "https://arxiv.org/pdf/2609.23034",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ehc8dxdh8mj40.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.23034",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23034"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Higher-order and non-geometric symmetries and Noether's theorem in k-cosymplectic Hamiltonian field theory",
  "title_text": "Higher-order and non-geometric symmetries and Noether's theorem in k-cosymplectic Hamiltonian field theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/ehc8dxdh8mj40",
  "venue": "arXiv",
  "versions": []
}