{"paper":{"title":"Torsion-free $H$-structures on almost Abelian solvmanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Marco Freibert","submitted_at":"2024-12-15T21:27:09Z","abstract_excerpt":"In this article, we provide a general set-up for arbitrary linear Lie groups $H\\leq \\mathrm{GL}(n,\\mathbb{R})$ which allows to characterise the almost Abelian Lie algebras admitting a torsion-free $H$-structure. In more concrete terms, using that an $n$-dimensional almost Abelian Lie algebra $\\mathfrak{g}=\\mathfrak{g}_f$ is fully determined by an endomorphism $f$ of $\\mathbb{R}^{n-1}$, we give a description of the subspace $\\mathcal{F}_{\\mathfrak{h}}$ of all $f\\in\\mathrm{End}(\\mathbb{R}^{n-1})$ for which $\\mathfrak{g}_f$ admits a ``special'' torsion-free $H$-structure in terms of the image of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11316","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.11316/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}