{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:JOFGH457MA6N2P6EGJQEX6JDVB","short_pith_number":"pith:JOFGH457","schema_version":"1.0","canonical_sha256":"4b8a63f3bf603cdd3fc432604bf923a8710c54bd1ce0826c3571673f3eb933da","source":{"kind":"arxiv","id":"2311.12583","version":1},"attestation_state":"computed","paper":{"title":"Root generated subalgebras of symmetrizable Kac-Moody algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RA","authors_text":"Deniz Kus, Irfan Habib, R. Venkatesh","submitted_at":"2023-11-21T13:03:47Z","abstract_excerpt":"The derived algebra of a symmetrizible Kac-Moody algebra $\\lie g$ is generated (as a Lie algebra) by its root spaces corresponding to real roots. In this paper, we address the natural reverse question: given any subset of real root vectors, is the Lie subalgebra of $\\lie g$ generated by these again the derived algebra of a Kac-Moody algebra? We call such Lie subalgebras root generated, give an affirmative answer to the above question and show that there is a one-to-one correspondence between them, real closed subroot systems and $\\pi$-systems contained in the positive system of $\\lie g$. Final"},"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":"2311.12583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2023-11-21T13:03:47Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"af6470717aa79180098a1acf5c23c2e7da11dfdcda82a087912aa3a66a9586b4","abstract_canon_sha256":"2e664d32e08900e0b8cad775952d281069a5855774c33df0b71f58fef0933bf4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:10:55.228156Z","signature_b64":"j0DmIRH/6s5yEjyRoTtYF2YOuotoJkAMf7K2fBNex/w12HafE7ejK4POgus7LTDvnXxZtM3087DnEFGowyz/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b8a63f3bf603cdd3fc432604bf923a8710c54bd1ce0826c3571673f3eb933da","last_reissued_at":"2026-06-10T01:10:55.227367Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:10:55.227367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Root generated subalgebras of symmetrizable Kac-Moody algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RA","authors_text":"Deniz Kus, Irfan Habib, R. Venkatesh","submitted_at":"2023-11-21T13:03:47Z","abstract_excerpt":"The derived algebra of a symmetrizible Kac-Moody algebra $\\lie g$ is generated (as a Lie algebra) by its root spaces corresponding to real roots. In this paper, we address the natural reverse question: given any subset of real root vectors, is the Lie subalgebra of $\\lie g$ generated by these again the derived algebra of a Kac-Moody algebra? We call such Lie subalgebras root generated, give an affirmative answer to the above question and show that there is a one-to-one correspondence between them, real closed subroot systems and $\\pi$-systems contained in the positive system of $\\lie g$. Final"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.12583","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.12583/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2311.12583","created_at":"2026-06-10T01:10:55.227494+00:00"},{"alias_kind":"arxiv_version","alias_value":"2311.12583v1","created_at":"2026-06-10T01:10:55.227494+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.12583","created_at":"2026-06-10T01:10:55.227494+00:00"},{"alias_kind":"pith_short_12","alias_value":"JOFGH457MA6N","created_at":"2026-06-10T01:10:55.227494+00:00"},{"alias_kind":"pith_short_16","alias_value":"JOFGH457MA6N2P6E","created_at":"2026-06-10T01:10:55.227494+00:00"},{"alias_kind":"pith_short_8","alias_value":"JOFGH457","created_at":"2026-06-10T01:10:55.227494+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/JOFGH457MA6N2P6EGJQEX6JDVB","json":"https://pith.science/pith/JOFGH457MA6N2P6EGJQEX6JDVB.json","graph_json":"https://pith.science/api/pith-number/JOFGH457MA6N2P6EGJQEX6JDVB/graph.json","events_json":"https://pith.science/api/pith-number/JOFGH457MA6N2P6EGJQEX6JDVB/events.json","paper":"https://pith.science/paper/JOFGH457"},"agent_actions":{"view_html":"https://pith.science/pith/JOFGH457MA6N2P6EGJQEX6JDVB","download_json":"https://pith.science/pith/JOFGH457MA6N2P6EGJQEX6JDVB.json","view_paper":"https://pith.science/paper/JOFGH457","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2311.12583&json=true","fetch_graph":"https://pith.science/api/pith-number/JOFGH457MA6N2P6EGJQEX6JDVB/graph.json","fetch_events":"https://pith.science/api/pith-number/JOFGH457MA6N2P6EGJQEX6JDVB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JOFGH457MA6N2P6EGJQEX6JDVB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JOFGH457MA6N2P6EGJQEX6JDVB/action/storage_attestation","attest_author":"https://pith.science/pith/JOFGH457MA6N2P6EGJQEX6JDVB/action/author_attestation","sign_citation":"https://pith.science/pith/JOFGH457MA6N2P6EGJQEX6JDVB/action/citation_signature","submit_replication":"https://pith.science/pith/JOFGH457MA6N2P6EGJQEX6JDVB/action/replication_record"}},"created_at":"2026-06-10T01:10:55.227494+00:00","updated_at":"2026-06-10T01:10:55.227494+00:00"}