{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MEHBGBU4IE3WOECAHOUDDBPSFX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"feb7cc576c5e892037b37daf36ca397333db730bc29338ab246a25e4dc4cdc47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-11-05T17:23:08Z","title_canon_sha256":"81983ad4794fa07a74961e919196af3cb7fdb946909c1d9b06a076dd8230b044"},"schema_version":"1.0","source":{"id":"1211.0936","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0936","created_at":"2026-05-18T02:52:47Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0936v2","created_at":"2026-05-18T02:52:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0936","created_at":"2026-05-18T02:52:47Z"},{"alias_kind":"pith_short_12","alias_value":"MEHBGBU4IE3W","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MEHBGBU4IE3WOECA","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MEHBGBU4","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:7d1df687573df281486f73b2dc351e7deb0b66159fd70c6aa6728a7b6a80d006","target":"graph","created_at":"2026-05-18T02:52:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we study the homogenized algebra $B$ of the enveloping algebra $U$ of the Lie algebra sl(2,C). We look first to connections between the category of graded left $B$- modules and the category of $U$-modules, then we prove $B$ is Koszul and Artin-Schelter regular of global dimension four, hence its Yoneda algebra $% B^{!}$ is selfinjective of radical five zero, the structure of $B^{!}$ is given. We describe next the category of homogenized Verma modules, which correspond to the lifting to $B$ of the usual Verma modules over $U$, and prove that such modules are Koszul of projective d","authors_text":"Roberto Martinez-Villa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-11-05T17:23:08Z","title":"The homogenized enveloping Algebra of the Lie Algebra sl(2,C)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0936","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:229ae635ef1a7f3320bae446f2e52468c4a44991e9d3f11ed67906fa682e39ba","target":"record","created_at":"2026-05-18T02:52:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"feb7cc576c5e892037b37daf36ca397333db730bc29338ab246a25e4dc4cdc47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-11-05T17:23:08Z","title_canon_sha256":"81983ad4794fa07a74961e919196af3cb7fdb946909c1d9b06a076dd8230b044"},"schema_version":"1.0","source":{"id":"1211.0936","kind":"arxiv","version":2}},"canonical_sha256":"610e13069c41376710403ba83185f22dde97dc857ba8a175b9841829bacf3103","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"610e13069c41376710403ba83185f22dde97dc857ba8a175b9841829bacf3103","first_computed_at":"2026-05-18T02:52:47.983541Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:47.983541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/2nKVvnyXF3xIPRS6NIHEgjoGWyAAdlw7dpEntX3mkV2JTmvyHFp15cSf/kyeYxDTX3MIZi6XcdA1b+TeZQSBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:47.984154Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0936","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:229ae635ef1a7f3320bae446f2e52468c4a44991e9d3f11ed67906fa682e39ba","sha256:7d1df687573df281486f73b2dc351e7deb0b66159fd70c6aa6728a7b6a80d006"],"state_sha256":"f1649ae625ca3be037770f44abed52dc3c88897d1c05931bd51b14ae1204c556"}