{"paper":{"title":"Wildness of the problems of classifying two-dimensional spaces of commuting linear operators and certain Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Anatolii P. Petravchuk, Tetiana Klymchuk, Vladimir V. Sergeichuk, Vyacheslav Futorny","submitted_at":"2017-09-29T11:23:53Z","abstract_excerpt":"For each two-dimensional vector space $V$ of commuting $n\\times n$ matrices over a field $\\mathbb F$ with at least 3 elements, we denote by $\\widetilde V$ the vector space of all $(n+1)\\times(n+1)$ matrices of the form $\\left[\\begin{smallmatrix}A&*\\\\0&0\\end{smallmatrix}\\right]$ with $A\\in V$. We prove the wildness of the problem of classifying Lie algebras $\\widetilde V$ with the bracket operation $[u,v]:=uv-vu$. We also prove the wildness of the problem of classifying two-dimensional vector spaces consisting of commuting linear operators on a vector space over a field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10334","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"}