{"paper":{"title":"The starred Dixmier's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Vered Moskowicz","submitted_at":"2013-10-28T19:58:22Z","abstract_excerpt":"Dixmier's famous question says the following: Is every algebra endomorphism of the first Weyl algebra, $A_1(F)$, where $F$ is a zero characteristic field, an automorphism? Let $\\alpha$ be the exchange involution on $A_1(F)$: $\\alpha(x)= y$, $\\alpha(y)= x$. An $\\alpha$-endomorphism of $A_1(F)$ is an endomorphism which preserves the involution $\\alpha$. Then one may ask the following question, which may be called the \"$\\alpha$-Dixmier's problem $1$\" or the \"starred Dixmier's problem $1$\": Is every $\\alpha$-endomorphism of $A_1(F)$ an automorphism?"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7562","kind":"arxiv","version":4},"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"}