{"paper":{"title":"An analogue of the Conjecture of Dixmier is true for the algebra of polynomial integro-differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RA","authors_text":"V. V. Bavula","submitted_at":"2010-11-12T18:57:12Z","abstract_excerpt":"Let $A_1:=K\\langle x, \\frac{d}{dx} \\rangle$ be the Weyl algebra and $\\mI_1:= K\\langle x, \\frac{d}{dx}, \\int \\rangle$ be the algebra of polynomial integro-differential operators over a field $K$ of characteristic zero. The Conjecture/Problem of Dixmier (1968) [still open]: {\\em is an algebra endomorphism of the Weyl algebra $A_1$ an automorphism?} The aim of the paper is to prove that {\\em each algebra endomorphism of the algebra $\\mI_1$ is an automorphism}. Notice that in contrast to the Weyl algebra $A_1$ the algebra $\\mI_1$ is a non-simple, non-Noetherian algebra which is not a domain. Moreo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3009","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"}