{"paper":{"title":"Versal Deformations and Versality in Central Extensions of Jacobi's Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Roger Carles, Toukaiddine Petit","submitted_at":"2010-09-03T15:10:21Z","abstract_excerpt":"Let $\\L_m$ be the scheme of the laws defined by the Jacobi's identities on $\\K^m$ with $\\K$ a field. A deformation of $\\g\\in\\L_m$, parametrized by a local $\\K$-algebra $\\A$, is a local $\\K$-algebra morphism from the local ring of $\\L_m$ at $\\phi_m$ to $\\A$. The problem to classify all the deformation equivalence classes of a Lie algebra with given base is solved by \"versal\" deformations. First, we give an algorithm for computing versal deformations. Second, we prove there is a bijection between the deformation equivalence classes of an algebraic Lie algebra $\\phi_m=\\mathrm{R}\\ltimes\\phi_n$ in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0696","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":""},"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"}