{
  "abstract": "Replacing the circle by a manifold leads to current Lie algebras and their central and derivation extensions. We separate the coefficient algebra, harmonic analysis and geometric data. Differentials modulo exact forms describe central extensions; divergence-free vector fields give explicit cocycles, whose compatible derivations satisfy a stabilizer equation. Compact examples include the three-sphere and its current--Virasoro extension. We also explain the analytic qualifications for SL(2,R) and its symmetric space and the role of transported multiplication in soft geometries. The recent harmonic constructions of Campoamor-Stursberg, Marrani and Rausch de Traubenberg are compared with the cohomological work of Coquereaux, Frappat, Ragoucy and Sorba and Castellani's loop geometry and infinite-dimensional free differential algebras. A coefficient-algebra construction connects currents to higher brackets and clarifies the additional requirements of a dynamical theory. For Lie algebras of order F, central extensions obey coupled binary and symmetric F-ary conditions, with explicit examples and obstructions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17781",
  "author_total": 3,
  "authors": [
    {
      "name": "R. Campoamor-Stursberg"
    },
    {
      "name": "A. Marrani"
    },
    {
      "name": "M. Rausch de Traubenberg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1nhbk0500pbqd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17781",
  "fulltext_url": null,
  "id": "1nhbk0500pbqd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17781",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.RT"
    ],
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      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7221812205",
  "pdf_url": "https://arxiv.org/pdf/2610.17781",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1nhbk0500pbqd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2610.17781",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17781"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Beyond the circle: current algebras, geometry and higher gauge structures",
  "title_text": "Beyond the circle: current algebras, geometry and higher gauge structures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/1nhbk0500pbqd",
  "venue": "arXiv",
  "versions": []
}