{
  "abstract": "We study KMS and ground states of the tame $C^*$-algebras $\\mathcal{O}_{m,n}$ of Ara, Exel and Katsura under the dynamics $σ_t(s_i)=m^{it}s_i$, $σ_t(t_j)=n^{it}t_j$. Normalized restriction to the full corner $A=q\\mathcal{O}_{m,n}q$, generated by the partial isometries $v_{ij}=s_i^{*}t_j$ of common energy $\\log(n/m)$, is at each inverse temperature $β$ an affine weak-$*$ homeomorphism of the two systems. Let $m,n\\ge 2$. When $m=n$ the corner dynamics is trivial, so the KMS simplices are identified with trace simplices. When $m\\neq n$, KMS states occur only at $β=1$, and there they are not unique. Conformal branching models surject the KMS$_1$ simplex onto a transportation polytope of dimension $(m-1)(n-1)$, whose vertices lift to extremal, hence factorial, KMS$_1$ states, the fibre over each vertex being itself the KMS$_1$ simplex of a quotient of $A$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30544",
  "author_total": 2,
  "authors": [
    {
      "name": "Paulo R. Pinto"
    },
    {
      "name": "Filipe Viseu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7m14nfs2v27mm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30544",
  "fulltext_url": null,
  "id": "7m14nfs2v27mm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30544",
  "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.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7214645271",
  "pdf_url": "https://arxiv.org/pdf/2609.30544",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7m14nfs2v27mm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30544",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30544"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "KMS and ground states for the normalized dynamics of the tame $C^*$-algebras $\\mathcal{O}_{m,n}$",
  "title_text": "KMS and ground states for the normalized dynamics of the tame C^*-algebras 𝒪_m,n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/7m14nfs2v27mm",
  "venue": "arXiv",
  "versions": []
}