{
  "abstract": "In this paper, we introduce the controlling $L_{\\infty}[1]$-algebra of extended Rota-Baxter algebras. As applications, we obtain the cohomology of extended Rota-Baxter algebras and homotopy extended Rota-Baxter algebras. We also study abelian extensions and formal deformations by the lower cohomology group. Lastly, we describe the intrinsic relationship among extended Rota-Baxter algebras, extended Rota-Baxter Lie algebras, and the eigenvalues of the extended Rota-Baxter operator. As the generalization of Rota-Baxter algebras with weight and modified Rota-Baxter algebras, the corresponding results also hold for those algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01304",
  "author_total": 1,
  "authors": [
    {
      "name": "Jian Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3q6apex391twa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01304",
  "fulltext_url": null,
  "id": "3q6apex391twa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01304",
  "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.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7206176953",
  "pdf_url": "https://arxiv.org/pdf/2609.01304",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3q6apex391twa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2609.01304",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01304"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Deformation theory and the controlling $L_{\\infty}$-structure of extended Rota-Baxter algebras",
  "title_text": "Deformation theory and the controlling L_∞-structure of extended Rota-Baxter algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/3q6apex391twa",
  "venue": "arXiv",
  "versions": []
}