{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:J5ITOXZ4K2SMQCLBTUON3RGSAI","short_pith_number":"pith:J5ITOXZ4","schema_version":"1.0","canonical_sha256":"4f51375f3c56a4c809619d1cddc4d20203462c1f15c68c0e67301fd62b975cdb","source":{"kind":"arxiv","id":"1610.00776","version":2},"attestation_state":"computed","paper":{"title":"Generalised Witt algebras and idealizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Susan J. Sierra, \\v{S}pela \\v{S}penko","submitted_at":"2016-10-03T22:35:47Z","abstract_excerpt":"Let $\\Bbbk$ be an algebraically closed field of characteristic zero, and let $\\Gamma$ be an additive subgroup of $\\Bbbk$. Results of Kaplansky-Santharoubane and Su classify intermediate series representations of the generalised Witt algebra $W_\\Gamma$ in terms of three families, one parameterised by ${\\mathbb A}^2$ and two by ${\\mathbb P}^1$. In this note, we use the first family to construct a homomorphism $\\Phi$ from the enveloping algebra $U(W_\\Gamma)$ to a skew extension of ${\\Bbbk}[a,b]$. We show that the image of $\\Phi$ is contained in a (double) idealizer subring of this skew extension "},"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":"1610.00776","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-10-03T22:35:47Z","cross_cats_sorted":[],"title_canon_sha256":"b22c9967786656e0adafc0dd29db6471e6e2d17d0e56434a3a841b0d75689949","abstract_canon_sha256":"5fea4543fb1484a15b237a9ed3879750b35640b2cf0dc756fe025c165fe11cca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:39.605428Z","signature_b64":"CnGtXDrxnnCbyAqwU3FGSZLFVhBmmqYZ8o3oDFNmQT3y7V0kqC7d9PP7PJRxBBcPk5LbOctJ2aFecZXWhU2bBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f51375f3c56a4c809619d1cddc4d20203462c1f15c68c0e67301fd62b975cdb","last_reissued_at":"2026-05-18T00:46:39.604766Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:39.604766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalised Witt algebras and idealizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Susan J. Sierra, \\v{S}pela \\v{S}penko","submitted_at":"2016-10-03T22:35:47Z","abstract_excerpt":"Let $\\Bbbk$ be an algebraically closed field of characteristic zero, and let $\\Gamma$ be an additive subgroup of $\\Bbbk$. Results of Kaplansky-Santharoubane and Su classify intermediate series representations of the generalised Witt algebra $W_\\Gamma$ in terms of three families, one parameterised by ${\\mathbb A}^2$ and two by ${\\mathbb P}^1$. In this note, we use the first family to construct a homomorphism $\\Phi$ from the enveloping algebra $U(W_\\Gamma)$ to a skew extension of ${\\Bbbk}[a,b]$. We show that the image of $\\Phi$ is contained in a (double) idealizer subring of this skew extension "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00776","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":"1610.00776","created_at":"2026-05-18T00:46:39.604869+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.00776v2","created_at":"2026-05-18T00:46:39.604869+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00776","created_at":"2026-05-18T00:46:39.604869+00:00"},{"alias_kind":"pith_short_12","alias_value":"J5ITOXZ4K2SM","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"J5ITOXZ4K2SMQCLB","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"J5ITOXZ4","created_at":"2026-05-18T12:30:22.444734+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/J5ITOXZ4K2SMQCLBTUON3RGSAI","json":"https://pith.science/pith/J5ITOXZ4K2SMQCLBTUON3RGSAI.json","graph_json":"https://pith.science/api/pith-number/J5ITOXZ4K2SMQCLBTUON3RGSAI/graph.json","events_json":"https://pith.science/api/pith-number/J5ITOXZ4K2SMQCLBTUON3RGSAI/events.json","paper":"https://pith.science/paper/J5ITOXZ4"},"agent_actions":{"view_html":"https://pith.science/pith/J5ITOXZ4K2SMQCLBTUON3RGSAI","download_json":"https://pith.science/pith/J5ITOXZ4K2SMQCLBTUON3RGSAI.json","view_paper":"https://pith.science/paper/J5ITOXZ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.00776&json=true","fetch_graph":"https://pith.science/api/pith-number/J5ITOXZ4K2SMQCLBTUON3RGSAI/graph.json","fetch_events":"https://pith.science/api/pith-number/J5ITOXZ4K2SMQCLBTUON3RGSAI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J5ITOXZ4K2SMQCLBTUON3RGSAI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J5ITOXZ4K2SMQCLBTUON3RGSAI/action/storage_attestation","attest_author":"https://pith.science/pith/J5ITOXZ4K2SMQCLBTUON3RGSAI/action/author_attestation","sign_citation":"https://pith.science/pith/J5ITOXZ4K2SMQCLBTUON3RGSAI/action/citation_signature","submit_replication":"https://pith.science/pith/J5ITOXZ4K2SMQCLBTUON3RGSAI/action/replication_record"}},"created_at":"2026-05-18T00:46:39.604869+00:00","updated_at":"2026-05-18T00:46:39.604869+00:00"}