{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:LWWW4KR5SPKTO5E75EUPBIHIOM","short_pith_number":"pith:LWWW4KR5","schema_version":"1.0","canonical_sha256":"5dad6e2a3d93d537749fe928f0a0e87329822f2b7a9f0e4f250821d642b98286","source":{"kind":"arxiv","id":"1607.05973","version":1},"attestation_state":"computed","paper":{"title":"Universal enveloping algebras and Poincar\\'e-Birkhoff-Witt theorem for involutive Hom-Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Bin Zhang, Li Guo, Shanghua Zheng","submitted_at":"2016-07-20T14:29:03Z","abstract_excerpt":"A Hom-type algebra is called involutive if its Hom map is multiplicative and involutive. In this paper, we obtain an explicit construction of the free involutive Hom-associative algebra on a Hom-module. We then apply this construction to obtain the universal enveloping algebra of an involutive Hom-Lie algebra. Finally we obtain a Poincar\\'e-Birkhoff-Witt theorem for the enveloping associative algebra of an involutive Hom-Lie 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":"1607.05973","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-20T14:29:03Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"1821b3cd718e914b022bbd4f888521d323a5baf64207a6960ea03d79086db502","abstract_canon_sha256":"087f561d1dd32caff869f4a4bc360fd3c85e959585215b9875476870648aff3d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:59.463255Z","signature_b64":"QIrauBSZu9DCkJ9vc7ypQuyUOgK6MsNrn17qU9w7i3pbhgumUKF+X5dSpLvDdhtj6INau1lN2+TOPHPFCKroDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5dad6e2a3d93d537749fe928f0a0e87329822f2b7a9f0e4f250821d642b98286","last_reissued_at":"2026-05-18T00:19:59.462667Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:59.462667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universal enveloping algebras and Poincar\\'e-Birkhoff-Witt theorem for involutive Hom-Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Bin Zhang, Li Guo, Shanghua Zheng","submitted_at":"2016-07-20T14:29:03Z","abstract_excerpt":"A Hom-type algebra is called involutive if its Hom map is multiplicative and involutive. In this paper, we obtain an explicit construction of the free involutive Hom-associative algebra on a Hom-module. We then apply this construction to obtain the universal enveloping algebra of an involutive Hom-Lie algebra. Finally we obtain a Poincar\\'e-Birkhoff-Witt theorem for the enveloping associative algebra of an involutive Hom-Lie algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05973","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":"1607.05973","created_at":"2026-05-18T00:19:59.462748+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.05973v1","created_at":"2026-05-18T00:19:59.462748+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05973","created_at":"2026-05-18T00:19:59.462748+00:00"},{"alias_kind":"pith_short_12","alias_value":"LWWW4KR5SPKT","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"LWWW4KR5SPKTO5E7","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"LWWW4KR5","created_at":"2026-05-18T12:30:29.479603+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/LWWW4KR5SPKTO5E75EUPBIHIOM","json":"https://pith.science/pith/LWWW4KR5SPKTO5E75EUPBIHIOM.json","graph_json":"https://pith.science/api/pith-number/LWWW4KR5SPKTO5E75EUPBIHIOM/graph.json","events_json":"https://pith.science/api/pith-number/LWWW4KR5SPKTO5E75EUPBIHIOM/events.json","paper":"https://pith.science/paper/LWWW4KR5"},"agent_actions":{"view_html":"https://pith.science/pith/LWWW4KR5SPKTO5E75EUPBIHIOM","download_json":"https://pith.science/pith/LWWW4KR5SPKTO5E75EUPBIHIOM.json","view_paper":"https://pith.science/paper/LWWW4KR5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.05973&json=true","fetch_graph":"https://pith.science/api/pith-number/LWWW4KR5SPKTO5E75EUPBIHIOM/graph.json","fetch_events":"https://pith.science/api/pith-number/LWWW4KR5SPKTO5E75EUPBIHIOM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LWWW4KR5SPKTO5E75EUPBIHIOM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LWWW4KR5SPKTO5E75EUPBIHIOM/action/storage_attestation","attest_author":"https://pith.science/pith/LWWW4KR5SPKTO5E75EUPBIHIOM/action/author_attestation","sign_citation":"https://pith.science/pith/LWWW4KR5SPKTO5E75EUPBIHIOM/action/citation_signature","submit_replication":"https://pith.science/pith/LWWW4KR5SPKTO5E75EUPBIHIOM/action/replication_record"}},"created_at":"2026-05-18T00:19:59.462748+00:00","updated_at":"2026-05-18T00:19:59.462748+00:00"}