{"paper":{"title":"Explicit class of finite-dimensional polynomial algebras with Wronskians over $\\mathbb{R}^d$ as $N$-ary Lie brackets: beyond $\\mathfrak{sl}(2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.QA"],"primary_cat":"math.RA","authors_text":"Arthemy V. Kiselev, Markuss G. \\c{K}\\=eni\\c{n}\\v{s}","submitted_at":"2026-05-26T17:14:29Z","abstract_excerpt":"Lie algebra $\\mathfrak{sl}(2)$ can be realised by vector fields on $\\mathbb{R}^1\\ni x$ with polynomial coefficients $1$, $-2x$, $-x^2$; their Wronskian determinants yield the Lie bracket. Likewise, the monomials $1$, $\\ldots$, $x^k/k!$, $\\ldots$, $x^N/N!$ span finite-dimensional strong homotopy (SH) Lie algebras with the Wronskians $\\mathbf{1} \\wedge \\partial_x \\wedge \\ldots \\wedge \\partial_x^{N-1}$ as the $N$-ary brackets. Over dimension $d=2$ with $\\mathbb{R}^2\\ni(x,y)$ and for the generalised complete Wronskian $W^{d=2}_{k=1}=\\mathbf{1}\\wedge \\partial_x \\wedge \\partial_y$ of differential or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27305","kind":"arxiv","version":1},"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/2605.27305/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"}