{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:2P5UYDPRZ6TCWMT7LMTYJAYE5T","short_pith_number":"pith:2P5UYDPR","schema_version":"1.0","canonical_sha256":"d3fb4c0df1cfa62b327f5b27848304ecf69e052be8e5083758b3962441e4b098","source":{"kind":"arxiv","id":"1009.1123","version":5},"attestation_state":"computed","paper":{"title":"Invariant generalized complex structures on Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dmitri V. Alekseevsky, Liana David","submitted_at":"2010-09-06T18:48:09Z","abstract_excerpt":"We describe a class (called regular) of invariant generalized complex structures on a real semisimple Lie group G. The problem reduces to the description of admissible pairs (\\gk, \\omega), where \\gk is an appropriate regular subalgebra of the complex Lie algebra \\gg^{C} associated to G and \\omega is a closed 2-form on \\gk, such that a non-degeneracy condition holds.\n  In the case when G is a semisimple Lie group of inner type (in particular, when G is compact) a classification of regular generalized complex structures on G is given. We show that any invariant generalized complex structure on a"},"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":"1009.1123","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-06T18:48:09Z","cross_cats_sorted":[],"title_canon_sha256":"4f777b8193b9528add3b24e5b9cb517deed3b076505e3c44568e4c9a1533499f","abstract_canon_sha256":"c44b66308726cc9c58d54938d3786af9bdd751700fa72671d2ff3b912f3914c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:01.818936Z","signature_b64":"MPZ3MxUxR/ktBT82jmtFUCzUeonosM6F3ukAqY7nSaUn1THMtYrAHsWikenUctm6ixX2z3NJXZZ/9HbApGdyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3fb4c0df1cfa62b327f5b27848304ecf69e052be8e5083758b3962441e4b098","last_reissued_at":"2026-05-18T02:58:01.818412Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:01.818412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariant generalized complex structures on Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dmitri V. Alekseevsky, Liana David","submitted_at":"2010-09-06T18:48:09Z","abstract_excerpt":"We describe a class (called regular) of invariant generalized complex structures on a real semisimple Lie group G. The problem reduces to the description of admissible pairs (\\gk, \\omega), where \\gk is an appropriate regular subalgebra of the complex Lie algebra \\gg^{C} associated to G and \\omega is a closed 2-form on \\gk, such that a non-degeneracy condition holds.\n  In the case when G is a semisimple Lie group of inner type (in particular, when G is compact) a classification of regular generalized complex structures on G is given. We show that any invariant generalized complex structure on a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1123","kind":"arxiv","version":5},"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":"1009.1123","created_at":"2026-05-18T02:58:01.818494+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.1123v5","created_at":"2026-05-18T02:58:01.818494+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1123","created_at":"2026-05-18T02:58:01.818494+00:00"},{"alias_kind":"pith_short_12","alias_value":"2P5UYDPRZ6TC","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"2P5UYDPRZ6TCWMT7","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"2P5UYDPR","created_at":"2026-05-18T12:26:03.138858+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/2P5UYDPRZ6TCWMT7LMTYJAYE5T","json":"https://pith.science/pith/2P5UYDPRZ6TCWMT7LMTYJAYE5T.json","graph_json":"https://pith.science/api/pith-number/2P5UYDPRZ6TCWMT7LMTYJAYE5T/graph.json","events_json":"https://pith.science/api/pith-number/2P5UYDPRZ6TCWMT7LMTYJAYE5T/events.json","paper":"https://pith.science/paper/2P5UYDPR"},"agent_actions":{"view_html":"https://pith.science/pith/2P5UYDPRZ6TCWMT7LMTYJAYE5T","download_json":"https://pith.science/pith/2P5UYDPRZ6TCWMT7LMTYJAYE5T.json","view_paper":"https://pith.science/paper/2P5UYDPR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.1123&json=true","fetch_graph":"https://pith.science/api/pith-number/2P5UYDPRZ6TCWMT7LMTYJAYE5T/graph.json","fetch_events":"https://pith.science/api/pith-number/2P5UYDPRZ6TCWMT7LMTYJAYE5T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2P5UYDPRZ6TCWMT7LMTYJAYE5T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2P5UYDPRZ6TCWMT7LMTYJAYE5T/action/storage_attestation","attest_author":"https://pith.science/pith/2P5UYDPRZ6TCWMT7LMTYJAYE5T/action/author_attestation","sign_citation":"https://pith.science/pith/2P5UYDPRZ6TCWMT7LMTYJAYE5T/action/citation_signature","submit_replication":"https://pith.science/pith/2P5UYDPRZ6TCWMT7LMTYJAYE5T/action/replication_record"}},"created_at":"2026-05-18T02:58:01.818494+00:00","updated_at":"2026-05-18T02:58:01.818494+00:00"}