{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YJGD3E3WZJG7PFGIPZA4X2DZKD","short_pith_number":"pith:YJGD3E3W","schema_version":"1.0","canonical_sha256":"c24c3d9376ca4df794c87e41cbe87950ede5ad816b430823e8c0d9629b22afa0","source":{"kind":"arxiv","id":"1411.3734","version":1},"attestation_state":"computed","paper":{"title":"Isomorphism invariants of enveloping algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.RA","authors_text":"Hamid Usefi","submitted_at":"2014-11-13T21:01:17Z","abstract_excerpt":"Let $L$ be a Lie algebra with its enveloping algebra $U(L)$ over a field. In this paper we survey results concerning the isomorphism problem for enveloping algebras: given another Lie algebra $H$ for which $U(L)$ and $U(H)$ are isomorphic as associative algebras, can we deduce that $L$ and $H$ are isomorphic Lie algebras? Over a field of positive characteristic we consider a similar problem for restricted Lie algebras, that is, given restricted Lie algebras $L$ and $H$ for which their restricted enveloping algebras are isomorphic as algebras, can we deduce that $L$ and $H$ are isomorphic?"},"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":"1411.3734","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-11-13T21:01:17Z","cross_cats_sorted":["math.GR","math.RT"],"title_canon_sha256":"99b11371f8bc3cb769163505cfe4d8c80ca0bc0f8640b33afb7465312881927a","abstract_canon_sha256":"3a38f9212dcc9613181d7ef0fe5b40df909c6af10c84933c94adf013a11a3864"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:37.858157Z","signature_b64":"NroLkfYFQuwDJu4MJOWQmhPd+cEbH8cil0uDxUhOGKrUuMqH+HKpOAMItmMVdDQO/xmG6JN7F3a4wHn2kJ6VAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c24c3d9376ca4df794c87e41cbe87950ede5ad816b430823e8c0d9629b22afa0","last_reissued_at":"2026-05-18T02:37:37.857714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:37.857714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isomorphism invariants of enveloping algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.RA","authors_text":"Hamid Usefi","submitted_at":"2014-11-13T21:01:17Z","abstract_excerpt":"Let $L$ be a Lie algebra with its enveloping algebra $U(L)$ over a field. In this paper we survey results concerning the isomorphism problem for enveloping algebras: given another Lie algebra $H$ for which $U(L)$ and $U(H)$ are isomorphic as associative algebras, can we deduce that $L$ and $H$ are isomorphic Lie algebras? Over a field of positive characteristic we consider a similar problem for restricted Lie algebras, that is, given restricted Lie algebras $L$ and $H$ for which their restricted enveloping algebras are isomorphic as algebras, can we deduce that $L$ and $H$ are isomorphic?"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3734","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":"1411.3734","created_at":"2026-05-18T02:37:37.857777+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.3734v1","created_at":"2026-05-18T02:37:37.857777+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3734","created_at":"2026-05-18T02:37:37.857777+00:00"},{"alias_kind":"pith_short_12","alias_value":"YJGD3E3WZJG7","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"YJGD3E3WZJG7PFGI","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"YJGD3E3W","created_at":"2026-05-18T12:28:57.508820+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/YJGD3E3WZJG7PFGIPZA4X2DZKD","json":"https://pith.science/pith/YJGD3E3WZJG7PFGIPZA4X2DZKD.json","graph_json":"https://pith.science/api/pith-number/YJGD3E3WZJG7PFGIPZA4X2DZKD/graph.json","events_json":"https://pith.science/api/pith-number/YJGD3E3WZJG7PFGIPZA4X2DZKD/events.json","paper":"https://pith.science/paper/YJGD3E3W"},"agent_actions":{"view_html":"https://pith.science/pith/YJGD3E3WZJG7PFGIPZA4X2DZKD","download_json":"https://pith.science/pith/YJGD3E3WZJG7PFGIPZA4X2DZKD.json","view_paper":"https://pith.science/paper/YJGD3E3W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.3734&json=true","fetch_graph":"https://pith.science/api/pith-number/YJGD3E3WZJG7PFGIPZA4X2DZKD/graph.json","fetch_events":"https://pith.science/api/pith-number/YJGD3E3WZJG7PFGIPZA4X2DZKD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YJGD3E3WZJG7PFGIPZA4X2DZKD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YJGD3E3WZJG7PFGIPZA4X2DZKD/action/storage_attestation","attest_author":"https://pith.science/pith/YJGD3E3WZJG7PFGIPZA4X2DZKD/action/author_attestation","sign_citation":"https://pith.science/pith/YJGD3E3WZJG7PFGIPZA4X2DZKD/action/citation_signature","submit_replication":"https://pith.science/pith/YJGD3E3WZJG7PFGIPZA4X2DZKD/action/replication_record"}},"created_at":"2026-05-18T02:37:37.857777+00:00","updated_at":"2026-05-18T02:37:37.857777+00:00"}