{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:7H7R3NOQDIBGKFUYP62LDG5DR7","short_pith_number":"pith:7H7R3NOQ","schema_version":"1.0","canonical_sha256":"f9ff1db5d01a026516987fb4b19ba38fea3afcc207cbe52794088ba96501ec57","source":{"kind":"arxiv","id":"1612.08051","version":1},"attestation_state":"computed","paper":{"title":"Lie structure of truncated symmetric Poisson algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ilana Zuila Monteiro Alves, Victor Petrogradsky","submitted_at":"2016-12-23T17:49:55Z","abstract_excerpt":"The paper naturally continues series of works on identical relations of group rings, enveloping algebras, and other related algebraic structures. Let $L$ be a Lie algebra over a field of characteristic $p>0$. Consider its symmetric algebra $S(L)=\\oplus_{n=0}^\\infty U_n/U_{n-1}$, which is isomorphic to a polynomial ring. It also has a structure of a Poisson algebra, where the Lie product is traditionally denoted by $\\{\\ ,\\ \\}$. This bracket naturally induces the structure of a Poisson algebra on the ring $\\mathbf{s}(L)=S(L)/(x^p\\,|\\, x\\in L)$, which we call a truncated symmetric Poisson algebra"},"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":"1612.08051","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-12-23T17:49:55Z","cross_cats_sorted":[],"title_canon_sha256":"cedc2167eb5e7b322c6e57960d1fd65fe92fbb11edd2cc4aaf66db1d2a1c3e25","abstract_canon_sha256":"e51267fa42e7f7fd54682763335814253880372ec6c8d1a121c64b91fd118c0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:52.694424Z","signature_b64":"Qs2nmdD4bKtSma2nI1gvwR84W1MqNAWVI96iFpWsDy1b4s5Y5BhaDvZzFpiRz7rKfSVC6VUowKNOHfH//WEqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9ff1db5d01a026516987fb4b19ba38fea3afcc207cbe52794088ba96501ec57","last_reissued_at":"2026-05-18T00:39:52.693754Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:52.693754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lie structure of truncated symmetric Poisson algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ilana Zuila Monteiro Alves, Victor Petrogradsky","submitted_at":"2016-12-23T17:49:55Z","abstract_excerpt":"The paper naturally continues series of works on identical relations of group rings, enveloping algebras, and other related algebraic structures. Let $L$ be a Lie algebra over a field of characteristic $p>0$. Consider its symmetric algebra $S(L)=\\oplus_{n=0}^\\infty U_n/U_{n-1}$, which is isomorphic to a polynomial ring. It also has a structure of a Poisson algebra, where the Lie product is traditionally denoted by $\\{\\ ,\\ \\}$. This bracket naturally induces the structure of a Poisson algebra on the ring $\\mathbf{s}(L)=S(L)/(x^p\\,|\\, x\\in L)$, which we call a truncated symmetric Poisson algebra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08051","kind":"arxiv","version":1},"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":"1612.08051","created_at":"2026-05-18T00:39:52.693850+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.08051v1","created_at":"2026-05-18T00:39:52.693850+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08051","created_at":"2026-05-18T00:39:52.693850+00:00"},{"alias_kind":"pith_short_12","alias_value":"7H7R3NOQDIBG","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"7H7R3NOQDIBGKFUY","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"7H7R3NOQ","created_at":"2026-05-18T12:30:04.600751+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/7H7R3NOQDIBGKFUYP62LDG5DR7","json":"https://pith.science/pith/7H7R3NOQDIBGKFUYP62LDG5DR7.json","graph_json":"https://pith.science/api/pith-number/7H7R3NOQDIBGKFUYP62LDG5DR7/graph.json","events_json":"https://pith.science/api/pith-number/7H7R3NOQDIBGKFUYP62LDG5DR7/events.json","paper":"https://pith.science/paper/7H7R3NOQ"},"agent_actions":{"view_html":"https://pith.science/pith/7H7R3NOQDIBGKFUYP62LDG5DR7","download_json":"https://pith.science/pith/7H7R3NOQDIBGKFUYP62LDG5DR7.json","view_paper":"https://pith.science/paper/7H7R3NOQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.08051&json=true","fetch_graph":"https://pith.science/api/pith-number/7H7R3NOQDIBGKFUYP62LDG5DR7/graph.json","fetch_events":"https://pith.science/api/pith-number/7H7R3NOQDIBGKFUYP62LDG5DR7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7H7R3NOQDIBGKFUYP62LDG5DR7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7H7R3NOQDIBGKFUYP62LDG5DR7/action/storage_attestation","attest_author":"https://pith.science/pith/7H7R3NOQDIBGKFUYP62LDG5DR7/action/author_attestation","sign_citation":"https://pith.science/pith/7H7R3NOQDIBGKFUYP62LDG5DR7/action/citation_signature","submit_replication":"https://pith.science/pith/7H7R3NOQDIBGKFUYP62LDG5DR7/action/replication_record"}},"created_at":"2026-05-18T00:39:52.693850+00:00","updated_at":"2026-05-18T00:39:52.693850+00:00"}