{
  "abstract": "We construct a bounded Hochschild one-cocycle which detects amenability of tracial states on unital C*-algebras. For an arbitrary trace the construction uses a faithful representation containing the GNS representation as a direct summand. When \\(τ\\) is faithful, \\(H_τ=L^2(A,τ)\\), and \\(J\\) is the canonical conjugation, the cocycle has the particularly simple form \\[ δ_τ(a)(x) =Jπ_τ(a^*)Jx-xJπ_τ(a^*)J. \\] It is inner in a natural Banach \\(A\\)-bimodule if and only if \\(τ\\) is amenable. We also give the corresponding reformulation of embeddability into an ultrapower of the hyperfinite \\(\\mathrm{II}_1\\) factor. Finally, for faithful traces we study a C*-algebraic variant of the Christensen--Sinclair two-cocycle and prove, with all admissibility details, that amenability makes this cocycle a coboundary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18756",
  "author_total": 1,
  "authors": [
    {
      "name": "Mehdi Moradi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6avv1dxrjpsvs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18756",
  "fulltext_url": null,
  "id": "6avv1dxrjpsvs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18756",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.18756",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6avv1dxrjpsvs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18756",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18756"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Cohomology of Amenable Traces",
  "title_text": "Cohomology of Amenable Traces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/6avv1dxrjpsvs",
  "venue": "arXiv",
  "versions": []
}