{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:QWQW23XPHOYJP66EQRMFN7INUF","short_pith_number":"pith:QWQW23XP","schema_version":"1.0","canonical_sha256":"85a16d6eef3bb097fbc4845856fd0da16fd90b7d2a65c46c2b9c54c3efd8b56f","source":{"kind":"arxiv","id":"1304.6003","version":2},"attestation_state":"computed","paper":{"title":"Poisson and Hochschild cohomology and the semiclassical limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Matthew Towers","submitted_at":"2013-04-22T16:12:51Z","abstract_excerpt":"Let $B$ be a quantum algebra possessing a semiclassical limit $A$. We show that under certain hypotheses $B^e$ can be thought of as a deformation of the Poisson enveloping algebra of $A$, and we give a criterion for the Hochschild cohomology of $B$ to be a deformation of the Poisson cohomology of $A$ in the case that $B$ is Koszul. We verify that condition for the algebra of $2\\times 2$ quantum matrices and calculate its Hochschild cohomology and the Poisson cohomology of its semiclassical limit."},"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":"1304.6003","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-04-22T16:12:51Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"a27b5ad5bec825aeee960c14e42b2e74251598bdf0728390a26d6be3072d0051","abstract_canon_sha256":"688338c1800d94af04ad3afd48497a61d197ea9f471139facb71e5ba2182b55c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:31.758281Z","signature_b64":"qFfKAJq/s/ziYYr58U6OmHwTfk37FwIDXFJl6zIs7ShwP8A/Dl/j8jqXJsWVI71bWPZDCm500Jw3dSKTIzV+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85a16d6eef3bb097fbc4845856fd0da16fd90b7d2a65c46c2b9c54c3efd8b56f","last_reissued_at":"2026-05-18T03:26:31.757690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:31.757690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Poisson and Hochschild cohomology and the semiclassical limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Matthew Towers","submitted_at":"2013-04-22T16:12:51Z","abstract_excerpt":"Let $B$ be a quantum algebra possessing a semiclassical limit $A$. We show that under certain hypotheses $B^e$ can be thought of as a deformation of the Poisson enveloping algebra of $A$, and we give a criterion for the Hochschild cohomology of $B$ to be a deformation of the Poisson cohomology of $A$ in the case that $B$ is Koszul. We verify that condition for the algebra of $2\\times 2$ quantum matrices and calculate its Hochschild cohomology and the Poisson cohomology of its semiclassical limit."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6003","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":"1304.6003","created_at":"2026-05-18T03:26:31.757779+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.6003v2","created_at":"2026-05-18T03:26:31.757779+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6003","created_at":"2026-05-18T03:26:31.757779+00:00"},{"alias_kind":"pith_short_12","alias_value":"QWQW23XPHOYJ","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"QWQW23XPHOYJP66E","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"QWQW23XP","created_at":"2026-05-18T12:27:57.521954+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/QWQW23XPHOYJP66EQRMFN7INUF","json":"https://pith.science/pith/QWQW23XPHOYJP66EQRMFN7INUF.json","graph_json":"https://pith.science/api/pith-number/QWQW23XPHOYJP66EQRMFN7INUF/graph.json","events_json":"https://pith.science/api/pith-number/QWQW23XPHOYJP66EQRMFN7INUF/events.json","paper":"https://pith.science/paper/QWQW23XP"},"agent_actions":{"view_html":"https://pith.science/pith/QWQW23XPHOYJP66EQRMFN7INUF","download_json":"https://pith.science/pith/QWQW23XPHOYJP66EQRMFN7INUF.json","view_paper":"https://pith.science/paper/QWQW23XP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.6003&json=true","fetch_graph":"https://pith.science/api/pith-number/QWQW23XPHOYJP66EQRMFN7INUF/graph.json","fetch_events":"https://pith.science/api/pith-number/QWQW23XPHOYJP66EQRMFN7INUF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QWQW23XPHOYJP66EQRMFN7INUF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QWQW23XPHOYJP66EQRMFN7INUF/action/storage_attestation","attest_author":"https://pith.science/pith/QWQW23XPHOYJP66EQRMFN7INUF/action/author_attestation","sign_citation":"https://pith.science/pith/QWQW23XPHOYJP66EQRMFN7INUF/action/citation_signature","submit_replication":"https://pith.science/pith/QWQW23XPHOYJP66EQRMFN7INUF/action/replication_record"}},"created_at":"2026-05-18T03:26:31.757779+00:00","updated_at":"2026-05-18T03:26:31.757779+00:00"}