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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1401.5141","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-21T01:26:02Z","cross_cats_sorted":[],"title_canon_sha256":"2a504cca249539cd84648d191bda6a2cb3d918c5051d44e0e6e950d24e65204a","abstract_canon_sha256":"5a8125a6157b19ee71455cdb9d829bc55531ac758544468c7f55acff011016ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:34.785083Z","signature_b64":"n4Nnk4+Weib0u1zQ0OytQH/NOB8a9cVufP52LCg5ydifrAxJ1MSXNtak484q0koWovfoz1jzqFdD+9gUR8anBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b59b53c56a5f9e47bedfc8d53a4e9855965788fde4dbb410fc2dc8638fbc376a","last_reissued_at":"2026-05-18T03:01:34.784576Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:34.784576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\alpha$. 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