{
  "abstract": "Rota-Baxter Lie groups are the group-level counterparts of Rota-Baxter Lie algebras of weight $1$. In this paper, we first establish a correspondence between representations of Rota-Baxter Lie groups and representations of Rota-Baxter Lie algebras of weight $1$ via differentiation and integration. We then develop a cohomology theory for Rota-Baxter Lie groups with coefficients in a representation by constructing an explicit cochain complex in arbitrary degrees. We justify this theory by proving a van Est type theorem, which relates the cohomology of a Rota-Baxter Lie group to that of its Rota-Baxter Lie algebra of weight $1$. As an application, we prove that equivalence classes of central extensions of a Rota-Baxter Lie group are classified by the second cohomology group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05216",
  "author_total": 1,
  "authors": [
    {
      "name": "Jun Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/106j6tm4smb24.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05216",
  "fulltext_url": null,
  "id": "106j6tm4smb24",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05216",
  "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.GR"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7220702955",
  "pdf_url": "https://arxiv.org/pdf/2610.05216",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/106j6tm4smb24.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.05216",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05216"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The van Est theorem for Rota-Baxter Lie groups",
  "title_text": "The van Est theorem for Rota-Baxter Lie groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/106j6tm4smb24",
  "venue": "arXiv",
  "versions": []
}