{
  "abstract": "Li proved that the noncommutative tori $A_θ$ and $A_{gθ}$ are strongly Morita equivalent whenever $g\\in\\mathrm{SO}(n,n|\\mathbb{Z})$ and $gθ$ is defined. We study equivariant extensions of these equivalences for canonical finite cyclic group actions. Let $W\\in\\mathrm{GL}_n(\\mathbb{Z})$ satisfy $W^tθW=θ$, $W^k=I_n$ and $1\\notin\\operatorname{spec}(W)$, and write $ρ(R)=\\operatorname{diag}(R,(R^t)^{-1})$. If $gρ(W^t)g^{-1}=ρ(P)$ for some $P\\in\\mathrm{GL}_n(\\mathbb{Z})$, we equip Li's $A_{gθ}$--$A_θ$ Heisenberg equivalence bimodule with a compatible $\\mathbb{Z}_k$-action. Consequently, the crossed products $A_{gθ}\\rtimes_{α_{P^t}}\\mathbb{Z}_k$ and $A_θ\\rtimes_{α_W}\\mathbb{Z}_k$ are strongly Morita equivalent. For the canonical flip action by $\\mathbb{Z}_2$, we prove that Morita equivalence of crossed products implies Morita equivalence of the underlying tori in every dimension, and prove the converse in dimensions two through four. For each fixed dimension $2\\leq n\\leq 4$, the complete invariants are the central rank and canonical $K_0$-trace range of the underlying torus, with the latter taken up to positive scaling. For the standard cyclic group actions of orders $2$, $3$, $4$ and $6$ on rotation algebras, we prove that the crossed products are Morita equivalent exactly when the action orders agree and the parameters lie in the same fractional-linear $\\mathrm{GL}_2(\\mathbb{Z})$-orbit, generalizing the result of Bönicke et al.\\ from irrational to arbitrary real parameters. We also construct infinite families of distinct parameters giving Morita-equivalent crossed products for each fixed $W$ satisfying the stated hypotheses.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38695",
  "author_total": 2,
  "authors": [
    {
      "name": "Sayan Chakraborty"
    },
    {
      "name": "Pratik Kumar Kundu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fpy93vnkvxfew.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38695",
  "fulltext_url": null,
  "id": "fpy93vnkvxfew",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38695",
  "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/2610.38695",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fpy93vnkvxfew.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38695",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38695"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Equivariant Morita equivalence for finite cyclic group actions on noncommutative tori",
  "title_text": "Equivariant Morita equivalence for finite cyclic group actions on noncommutative tori",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/fpy93vnkvxfew",
  "venue": "arXiv",
  "versions": []
}