{
  "abstract": "We study $p$-approximation properties of $\\ell^p$ uniform Roe algebras and their connections to coarse geometry and group theory. For bounded geometry metric spaces, property A implies $p$-nuclearity of $B_u^p(X)$ for $1<p<\\infty$, while $B_u^1(X)$ is always $1$-nuclear. Property A also yields coefficient characterizations and $p$-complete exactness results for $B_u^p(X,-)$; at $p=1$ these coefficient results hold without property A. We introduce the $p$-invariant translation approximation property and its operator space version. The $p$-AP implies a coefficient fixed-point identity for arbitrary $SQ_p$ coefficients, and for exact groups it is equivalent to the $p$-operator ITAP. At $p=1$, every discrete group satisfies the full coefficient fixed-point identity. We also establish coefficient permanence under subgroups, finite-index supergroups, and group extensions with $p$-AP quotient, including direct and semidirect products. In particular, the class of exact groups with the $p$-AP is closed under group extensions. We also obtain higher-rank lattices as examples failing the $p$-operator ITAP.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.27230",
  "author_total": 1,
  "authors": [
    {
      "name": "Yeong Chyuan Chung"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6haax5px5bfjw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.27230",
  "fulltext_url": null,
  "id": "6haax5px5bfjw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.27230",
  "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.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7166094797",
  "pdf_url": "https://arxiv.org/pdf/2606.27230",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6haax5px5bfjw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2606.27230",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.27230"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On some $p$-approximation properties of discrete groups and $\\ell^p$ uniform Roe algebras",
  "title_text": "On some p-approximation properties of discrete groups and ℓ^p uniform Roe algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/6haax5px5bfjw",
  "venue": "arXiv",
  "versions": []
}