{
  "abstract": "Let $(\\G,ρ,ω)$ be a symplectic Lie--Rinehart--Jacobi algebra over a commutative algebra $A$, equivalently a Lie--Rinehart algebra $(\\G,\\barρ)$ endowed with a $1$-cocycle $χ$ and a nondegenerate $2$-form closed for the twisted differential $d_ρ=d_{\\barρ}+χ\\wedge$. Starting from the standard extension by the $2$-cocycle $ω$, we study the strict lifting problem for its canonical $1$-form $η$ in the LRJ setting. We prove that the strict symmetries of $η$ are precisely the elements $X_f+fe$ and that $f\\mapsto X_f+fe$ identifies the Jacobi Lie algebra $(A,\\{\\,,\\})$ with this Lie algebra of strict symmetries. For locally Hamiltonian elements, the obstruction to a strict lift is the class $[i_xω]\\in H^1_ρ(\\G,A)$, yielding the exact sequence $0\\to\\ham\\to\\hamloc\\to H^1_ρ(\\G,A)\\to0$. We also relate Okassa's symplectic curl to the variation of $dη$ and establish a conformal triviality criterion. In the smooth case the framework reduces to locally conformally symplectic geometry, and on a closed surface of genus $g\\geq2$ we obtain structures that are not conformally trivial and whose obstruction space has dimension $2g-2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32370",
  "author_total": 3,
  "authors": [
    {
      "name": "Basile Guy Richard Bossoto"
    },
    {
      "name": "Servais Cyr Gatsé"
    },
    {
      "name": "Olivier Mabiala Mikanou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cw6rc0vnjgfmj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32370",
  "fulltext_url": null,
  "id": "cw6rc0vnjgfmj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32370",
  "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.DG"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7214803668",
  "pdf_url": "https://arxiv.org/pdf/2609.32370",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cw6rc0vnjgfmj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32370",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32370"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Strict lifts and cohomological obstructions in symplectic Lie--Rinehart--Jacobi prequantization",
  "title_text": "Strict lifts and cohomological obstructions in symplectic Lie--Rinehart--Jacobi prequantization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/cw6rc0vnjgfmj",
  "venue": "arXiv",
  "versions": []
}