{
  "abstract": "We prove that groups acting freely and cocompactly on (possibly exotic) affine buildings of type $\\tilde{A}_2$ and $\\tilde C_2$ are mixed-identity free and have selfless reduced $C^*$-algebras. These results follow from a strong form of ping-pong dynamics that we call 'transversal contractivity'. Our main geometric result regards domesticity properties of elements in the associated polygons at infinity: we prove that, in our context, the opposite geometry of a hyperbolic element is topologically large.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17129",
  "author_total": 3,
  "authors": [
    {
      "name": "Corentin Le Bars"
    },
    {
      "name": "Elyasheev Leibtag"
    },
    {
      "name": "Itamar Vigdorovich"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d6vnqnz8per6g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17129",
  "fulltext_url": null,
  "id": "d6vnqnz8per6g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17129",
  "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.GR"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7213407032",
  "pdf_url": "https://arxiv.org/pdf/2609.17129",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d6vnqnz8per6g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17129",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17129"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Selflessness, MIF and opposition in groups acting on exotic buildings",
  "title_text": "Selflessness, MIF and opposition in groups acting on exotic buildings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/d6vnqnz8per6g",
  "venue": "arXiv",
  "versions": []
}