{
  "abstract": "We study strong Morita equivalence for crossed products of noncommutative solenoids by cyclic groups. Using their description as twisted group $\\mathrm C^*$-algebras, we construct automorphisms induced by the natural linear action of $\\mathrm{SL}_2(\\mathbb Z[1/p])$ on $\\mathbb Z[1/p]^2$, for every integer $p>1$. For odd primes, we use the Heisenberg--Weyl representation to construct compatible cyclic group actions on the equivalence bimodules relating solenoids with reciprocal parameters. This yields strong Morita equivalences between the corresponding crossed products by $\\mathbb Z$ and, for finite-order matrices, by finite cyclic groups. The corresponding equivalence for flip crossed products for the action of $\\mathbb Z/2\\mathbb Z$ holds for every prime, including $2$. For prime $p$, we give representatives for the nontrivial finite subgroups of $\\mathrm{SL}_2(\\mathbb Z[1/p])$ and explicit arithmetic criteria for conjugacy among these representatives.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.03353",
  "author_total": 1,
  "authors": [
    {
      "name": "Pratik Kumar Kundu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1rhpe0s36d401.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.03353",
  "fulltext_url": null,
  "id": "1rhpe0s36d401",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.03353",
  "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",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7167579220",
  "pdf_url": "https://arxiv.org/pdf/2607.03353",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1rhpe0s36d401.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2607.03353",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.03353"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Heisenberg-Weyl Representations and Morita equivalence for crossed products of Noncommutative solenoids",
  "title_text": "Heisenberg-Weyl Representations and Morita equivalence for crossed products of Noncommutative solenoids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/1rhpe0s36d401",
  "venue": "arXiv",
  "versions": []
}