{"paper":{"title":"The starred Dixmier conjecture for $A_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Christian Valqui, Vered Moskowicz","submitted_at":"2014-01-21T01:26:02Z","abstract_excerpt":"Let $A_1(K)=K \\langle x,y | yx-xy= 1 \\rangle$ be the first Weyl algebra over a characteristic zero field $K$ and let $\\alpha$ be the exchange involution on $A_1(K)$ given by $\\alpha(x)= y$ and $\\alpha(y)= x$. The Dixmier conjecture of Dixmier (1968) asks: Is every algebra endomorphism of the Weyl algebra $A_1(K)$ an automorphism? The aim of this paper is to prove that each $\\alpha$-endomorphism of $A_1(K)$ is an automorphism. Here an $\\alpha$-endomorphism of $A_1(K)$ is an endomorphism which preserves the involution $\\alpha$. We also prove an analogue result for the Jacobian conjecture in dime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5141","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"}