{"paper":{"title":"Lie subalgebras of vector fields on curves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RA","authors_text":"Colin Ingalls, Lucas Buzaglo","submitted_at":"2026-06-19T21:04:47Z","abstract_excerpt":"We study the subalgebra structure of Krichever-Novikov algebras, which are Lie algebras of vector fields on smooth affine curves. Our main result is that every infinite-dimensional subalgebra of a Krichever-Novikov algebra is isomorphic to a finite-codimensional subalgebra of another Krichever-Novikov algebra.\n  We then present some applications of our main result. First, we show that the universal enveloping algebra of any such infinite-dimensional subalgebra is not noetherian. We then prove that all Krichever-Novikov algebras satisfy the Dixmier property that all their nonzero endomorphisms "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21748","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/2606.21748/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"}