{"paper":{"title":"Maximal dimensional subalgebras of general Cartan type Lie algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jason Bell, Lucas Buzaglo","submitted_at":"2023-11-10T11:26:40Z","abstract_excerpt":"Let $\\Bbbk$ be a field of characteristic zero and let $\\mathbb{W}_n = \\operatorname{Der}(\\Bbbk[x_1,\\cdots,x_n])$ be the $n^{\\text{th}}$ general Cartan type Lie algebra. In this paper, we study Lie subalgebras $L$ of $\\mathbb{W}_n$ of maximal Gelfand-Kirillov (GK) dimension, that is, with $\\operatorname{GKdim}(L) = n$.\n  For $n = 1$, we completely classify such $L$, proving a conjecture of the second author. As a corollary, we obtain a new proof that $\\mathbb{W}_1$ satisfies the Dixmier conjecture, in other words, $\\operatorname{End}(\\mathbb{W}_1) \\setminus \\{0\\} = \\operatorname{Aut}(\\mathbb{W}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.06001","kind":"arxiv","version":2},"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/2311.06001/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"}