{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:NRIBWOF4EFUOXIYZDTG5QYDM5X","short_pith_number":"pith:NRIBWOF4","schema_version":"1.0","canonical_sha256":"6c501b38bc2168eba3191ccdd8606cedebfc5bf5ca6771dfc13f54402e212fdf","source":{"kind":"arxiv","id":"1101.4305","version":2},"attestation_state":"computed","paper":{"title":"On the eigenvector algebra of the product of elements with commutator one in the first Weyl algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"V. V. Bavula","submitted_at":"2011-01-22T18:16:47Z","abstract_excerpt":"Let $A_1=K < X, Y | [Y,X]=1>$ be the (first) Weyl algebra over a field $K$ of characteristic zero. It is known that the set of eigenvalues of the inner derivation $\\ad (YX)$ of $A_1$ is $\\Z$. Let $ A_1\\ra A_1$, $X\\mapsto x$, $Y\\mapsto y$, be a $K$-algebra homomorphism, i.e. $[y,x]=1$. It is proved that the set of eigenvalues of the inner derivation $\\ad (yx)$ of the Weyl algebra $A_1$ is $\\Z$ and the eigenvector algebra of $\\ad (yx)$ is $K< x,y> $ (this would be an easy corollary of the Problem/Conjecture of Dixmier of 1968 [still open]: {\\em is an algebra endomorphism of $A_1$ an automorphism"},"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":"1101.4305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-01-22T18:16:47Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"19ac5ffbf4384d29b089a58c2fb1b070e4b88e8acbb2bc1283c691983d455661","abstract_canon_sha256":"0485b9cf69ba3502c32949156c21fcbf929f281a1efd084170e444974e07d7b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:25.331773Z","signature_b64":"8dmajgayPYmV1AER73+aptQLheEjqez710AJhyRoan06q8VP3CprNisaLR/oO/kc7teBjnwaA1h0F0G6fPOwBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c501b38bc2168eba3191ccdd8606cedebfc5bf5ca6771dfc13f54402e212fdf","last_reissued_at":"2026-05-18T02:03:25.331228Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:25.331228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the eigenvector algebra of the product of elements with commutator one in the first Weyl algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"V. V. Bavula","submitted_at":"2011-01-22T18:16:47Z","abstract_excerpt":"Let $A_1=K < X, Y | [Y,X]=1>$ be the (first) Weyl algebra over a field $K$ of characteristic zero. It is known that the set of eigenvalues of the inner derivation $\\ad (YX)$ of $A_1$ is $\\Z$. Let $ A_1\\ra A_1$, $X\\mapsto x$, $Y\\mapsto y$, be a $K$-algebra homomorphism, i.e. $[y,x]=1$. It is proved that the set of eigenvalues of the inner derivation $\\ad (yx)$ of the Weyl algebra $A_1$ is $\\Z$ and the eigenvector algebra of $\\ad (yx)$ is $K< x,y> $ (this would be an easy corollary of the Problem/Conjecture of Dixmier of 1968 [still open]: {\\em is an algebra endomorphism of $A_1$ an automorphism"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4305","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1101.4305","created_at":"2026-05-18T02:03:25.331300+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.4305v2","created_at":"2026-05-18T02:03:25.331300+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4305","created_at":"2026-05-18T02:03:25.331300+00:00"},{"alias_kind":"pith_short_12","alias_value":"NRIBWOF4EFUO","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"NRIBWOF4EFUOXIYZ","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"NRIBWOF4","created_at":"2026-05-18T12:26:37.096874+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NRIBWOF4EFUOXIYZDTG5QYDM5X","json":"https://pith.science/pith/NRIBWOF4EFUOXIYZDTG5QYDM5X.json","graph_json":"https://pith.science/api/pith-number/NRIBWOF4EFUOXIYZDTG5QYDM5X/graph.json","events_json":"https://pith.science/api/pith-number/NRIBWOF4EFUOXIYZDTG5QYDM5X/events.json","paper":"https://pith.science/paper/NRIBWOF4"},"agent_actions":{"view_html":"https://pith.science/pith/NRIBWOF4EFUOXIYZDTG5QYDM5X","download_json":"https://pith.science/pith/NRIBWOF4EFUOXIYZDTG5QYDM5X.json","view_paper":"https://pith.science/paper/NRIBWOF4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.4305&json=true","fetch_graph":"https://pith.science/api/pith-number/NRIBWOF4EFUOXIYZDTG5QYDM5X/graph.json","fetch_events":"https://pith.science/api/pith-number/NRIBWOF4EFUOXIYZDTG5QYDM5X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NRIBWOF4EFUOXIYZDTG5QYDM5X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NRIBWOF4EFUOXIYZDTG5QYDM5X/action/storage_attestation","attest_author":"https://pith.science/pith/NRIBWOF4EFUOXIYZDTG5QYDM5X/action/author_attestation","sign_citation":"https://pith.science/pith/NRIBWOF4EFUOXIYZDTG5QYDM5X/action/citation_signature","submit_replication":"https://pith.science/pith/NRIBWOF4EFUOXIYZDTG5QYDM5X/action/replication_record"}},"created_at":"2026-05-18T02:03:25.331300+00:00","updated_at":"2026-05-18T02:03:25.331300+00:00"}