{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DBPB7UEYK6OHZ3FU4I2BHPZG4X","short_pith_number":"pith:DBPB7UEY","schema_version":"1.0","canonical_sha256":"185e1fd098579c7cecb4e23413bf26e5c75ff72d85f76a976d7008c2b321bcbe","source":{"kind":"arxiv","id":"1512.03469","version":1},"attestation_state":"computed","paper":{"title":"Complete classification of $H$-type algebras: I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Irina Markina, Kenro Furutani","submitted_at":"2015-12-10T22:31:43Z","abstract_excerpt":"Let $\\mathscr N$ be a 2-step nilpotent Lie algebra endowed with non-degenerate scalar product $\\langle.\\,,.\\rangle$ and let $\\mathscr N=V\\oplus_{\\perp}Z$, where $Z$ is the centre of the Lie algebra and $V$ its orthogonal complement with respect to the scalar product. We study the classification of the Lie algebras for which the space $V$ arises as a representation space of a Clifford algebra $\\Cl(\\mathbb R^{r,s})$ and the representation map $J\\colon \\Cl(\\mathbb R^{r,s})\\to(V)$ is related to the Lie algebra structure by $\\langle J_zv,w\\rangle=\\langle z,[v,w]\\rangle$ for all $z\\in \\mathbb R^{r,s"},"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":"1512.03469","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-12-10T22:31:43Z","cross_cats_sorted":[],"title_canon_sha256":"85656f05b334078f95815ae27ef5a1dbd31ae083a3231affa9b01bb924a7594c","abstract_canon_sha256":"1bbb757a5f6648a3ee29723673478152942d06d50bf699eb85003947c643ec85"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:32.361106Z","signature_b64":"SdPj4e777zhmR4I1oXRq5+SaIjD4VVJSZV6Tq7sZk1gRP2EVrTS7IJaOH5TRJcQM2pIojI2AHeKjF5W3pYOABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"185e1fd098579c7cecb4e23413bf26e5c75ff72d85f76a976d7008c2b321bcbe","last_reissued_at":"2026-05-18T01:24:32.360471Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:32.360471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complete classification of $H$-type algebras: I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Irina Markina, Kenro Furutani","submitted_at":"2015-12-10T22:31:43Z","abstract_excerpt":"Let $\\mathscr N$ be a 2-step nilpotent Lie algebra endowed with non-degenerate scalar product $\\langle.\\,,.\\rangle$ and let $\\mathscr N=V\\oplus_{\\perp}Z$, where $Z$ is the centre of the Lie algebra and $V$ its orthogonal complement with respect to the scalar product. We study the classification of the Lie algebras for which the space $V$ arises as a representation space of a Clifford algebra $\\Cl(\\mathbb R^{r,s})$ and the representation map $J\\colon \\Cl(\\mathbb R^{r,s})\\to(V)$ is related to the Lie algebra structure by $\\langle J_zv,w\\rangle=\\langle z,[v,w]\\rangle$ for all $z\\in \\mathbb R^{r,s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03469","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":"1512.03469","created_at":"2026-05-18T01:24:32.360579+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.03469v1","created_at":"2026-05-18T01:24:32.360579+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03469","created_at":"2026-05-18T01:24:32.360579+00:00"},{"alias_kind":"pith_short_12","alias_value":"DBPB7UEYK6OH","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DBPB7UEYK6OHZ3FU","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DBPB7UEY","created_at":"2026-05-18T12:29:17.054201+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/DBPB7UEYK6OHZ3FU4I2BHPZG4X","json":"https://pith.science/pith/DBPB7UEYK6OHZ3FU4I2BHPZG4X.json","graph_json":"https://pith.science/api/pith-number/DBPB7UEYK6OHZ3FU4I2BHPZG4X/graph.json","events_json":"https://pith.science/api/pith-number/DBPB7UEYK6OHZ3FU4I2BHPZG4X/events.json","paper":"https://pith.science/paper/DBPB7UEY"},"agent_actions":{"view_html":"https://pith.science/pith/DBPB7UEYK6OHZ3FU4I2BHPZG4X","download_json":"https://pith.science/pith/DBPB7UEYK6OHZ3FU4I2BHPZG4X.json","view_paper":"https://pith.science/paper/DBPB7UEY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.03469&json=true","fetch_graph":"https://pith.science/api/pith-number/DBPB7UEYK6OHZ3FU4I2BHPZG4X/graph.json","fetch_events":"https://pith.science/api/pith-number/DBPB7UEYK6OHZ3FU4I2BHPZG4X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DBPB7UEYK6OHZ3FU4I2BHPZG4X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DBPB7UEYK6OHZ3FU4I2BHPZG4X/action/storage_attestation","attest_author":"https://pith.science/pith/DBPB7UEYK6OHZ3FU4I2BHPZG4X/action/author_attestation","sign_citation":"https://pith.science/pith/DBPB7UEYK6OHZ3FU4I2BHPZG4X/action/citation_signature","submit_replication":"https://pith.science/pith/DBPB7UEYK6OHZ3FU4I2BHPZG4X/action/replication_record"}},"created_at":"2026-05-18T01:24:32.360579+00:00","updated_at":"2026-05-18T01:24:32.360579+00:00"}