{
  "abstract": "Let $G=\\exp(\\g)$ be an exponential solvable Lie group, $π\\in\\widehat G$, and $Ω_π$ the coadjoint orbit attached to $π$ by the orbit method. The Zariski closure conjecture asserts that the Poisson characteristic variety $\\VA(π_ν)$ of the deformed representation coincides with the Zariski closure of $Ω_π$ in $\\g^*$. Known until now only in special situations, including the nilpotent case, it is proved here in full generality. Since the Hilbert space of $π$ is a quantization of the symplectic manifold $Ω_π$, the statement says that the passage back from the representation to the orbit, a dequantization, loses nothing: the orbit is recovered, up to Zariski closure, from the algebra alone. We also characterize the quasi-Frobenius exponential Lie algebras, those whose dual vector space is a Zariski-dense coadjoint orbit, through the triviality of the annihilator of an irreducible representation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00757",
  "author_total": 1,
  "authors": [
    {
      "name": "Ali Baklouti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8pb54gxyfrsae.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00757",
  "fulltext_url": null,
  "id": "8pb54gxyfrsae",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00757",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00757",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8pb54gxyfrsae.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00757",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00757"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A proof of the Zariski closure conjecture and quasi-Frobenius exponential algebras",
  "title_text": "A proof of the Zariski closure conjecture and quasi-Frobenius exponential algebras",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/8pb54gxyfrsae",
  "venue": "arXiv",
  "versions": []
}