{"paper":{"title":"Locally finite solvable Lie algebras of derivations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Solvable Lie subalgebras generated by locally finite ones are locally finite for the affine plane under an extra assumption.","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mikhail Zaidenberg","submitted_at":"2026-04-03T08:30:14Z","abstract_excerpt":"Let X be an affine variety and L be a solvable Lie subalgebra of Lie(Aut(X)) generated by a finite collection of locally finite Lie subalgebras. The authors of [arXiv:2507.09679] wondered whether L is itself locally finite. Here we present some criteria for the local finiteness of L. Under some additional assumption, we answer this question in the affirmative in the particular case where X is the affine plane."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Under some additional assumption, we answer this question in the affirmative in the particular case where X is the affine plane.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The additional assumption (unspecified in the abstract) that is required to obtain the affirmative answer for the affine plane.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Criteria are given for local finiteness of solvable Lie algebras of derivations on affine varieties, with an affirmative answer for the affine plane under an additional assumption.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Solvable Lie subalgebras generated by locally finite ones are locally finite for the affine plane under an extra assumption.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ad48a45ab3e66cd0c741f47199b2a25c41e60f14f4aa6b7c1a4b4af8b2bcd76c"},"source":{"id":"2604.02864","kind":"arxiv","version":4},"verdict":{"id":"52d0375f-4a9f-4f56-99aa-e8202ed70b3c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T18:23:19.294295Z","strongest_claim":"Under some additional assumption, we answer this question in the affirmative in the particular case where X is the affine plane.","one_line_summary":"Criteria are given for local finiteness of solvable Lie algebras of derivations on affine varieties, with an affirmative answer for the affine plane under an additional assumption.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The additional assumption (unspecified in the abstract) that is required to obtain the affirmative answer for the affine plane.","pith_extraction_headline":"Solvable Lie subalgebras generated by locally finite ones are locally finite for the affine plane under an extra assumption."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.02864/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"}