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We show that $\\limfunc{gldim}(U(\\mathcal{L}_{+}))= \\limfunc{lFPD}(U(\\mathcal{L}))= \\limfunc{rFPD}(U(\\mathcal{L}))= \\limfunc{injdim}_{U(\\mathcal{L})}(U(\\mathcal{L}))= \\dim (\\mathcal{L}_{+})$.\n  We also prove that $U(\\mathcal{L})$ is Auslander-Gorenstein and Cohen-Macaulay and thus that it has a QF classical quotient ring."},"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":"math/0506262","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.RA","submitted_at":"2005-06-14T00:44:31Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"6e8d57c4c383916ac3dbf6eb81052c227b928a896c5717f9bbe54e5ab9e42932","abstract_canon_sha256":"171fd613cb1aa670916d791428b12fd10b1da036b32fcc7d145b09e65e028c8f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:40:03.529528Z","signature_b64":"VPrY85dIqgI18Jovbb56bvW2qLLoo6m6yFIAUR449mRupxtFcbOj4L37KfZH1TGu7gTnkXwI14xalSSFc5ejAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64838743eb4309e726d257aae54b6f7740a1dd61c0ab2b90be70b86310c0bf8c","last_reissued_at":"2026-07-04T14:40:03.529162Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:40:03.529162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homological properties of color Lie superalgebras","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Kenneth L. Price","submitted_at":"2005-06-14T00:44:31Z","abstract_excerpt":"Let $\\mathcal{L}=\\mathcal{L}_{+}\\oplus \\mathcal{L}_{-}$ be a finite dimensional color Lie superalgebra over a field of characteristic 0 with universal enveloping algebra $U(\\mathcal{L})$. We show that $\\limfunc{gldim}(U(\\mathcal{L}_{+}))= \\limfunc{lFPD}(U(\\mathcal{L}))= \\limfunc{rFPD}(U(\\mathcal{L}))= \\limfunc{injdim}_{U(\\mathcal{L})}(U(\\mathcal{L}))= \\dim (\\mathcal{L}_{+})$.\n  We also prove that $U(\\mathcal{L})$ is Auslander-Gorenstein and Cohen-Macaulay and thus that it has a QF classical quotient ring."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506262","kind":"arxiv","version":2},"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/math/0506262/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":"math/0506262","created_at":"2026-07-04T14:40:03.529223+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0506262v2","created_at":"2026-07-04T14:40:03.529223+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506262","created_at":"2026-07-04T14:40:03.529223+00:00"},{"alias_kind":"pith_short_12","alias_value":"MSBYOQ7LIME6","created_at":"2026-07-04T14:40:03.529223+00:00"},{"alias_kind":"pith_short_16","alias_value":"MSBYOQ7LIME6OJWS","created_at":"2026-07-04T14:40:03.529223+00:00"},{"alias_kind":"pith_short_8","alias_value":"MSBYOQ7L","created_at":"2026-07-04T14:40:03.529223+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/MSBYOQ7LIME6OJWSK6VOKS3PO5","json":"https://pith.science/pith/MSBYOQ7LIME6OJWSK6VOKS3PO5.json","graph_json":"https://pith.science/api/pith-number/MSBYOQ7LIME6OJWSK6VOKS3PO5/graph.json","events_json":"https://pith.science/api/pith-number/MSBYOQ7LIME6OJWSK6VOKS3PO5/events.json","paper":"https://pith.science/paper/MSBYOQ7L"},"agent_actions":{"view_html":"https://pith.science/pith/MSBYOQ7LIME6OJWSK6VOKS3PO5","download_json":"https://pith.science/pith/MSBYOQ7LIME6OJWSK6VOKS3PO5.json","view_paper":"https://pith.science/paper/MSBYOQ7L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0506262&json=true","fetch_graph":"https://pith.science/api/pith-number/MSBYOQ7LIME6OJWSK6VOKS3PO5/graph.json","fetch_events":"https://pith.science/api/pith-number/MSBYOQ7LIME6OJWSK6VOKS3PO5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MSBYOQ7LIME6OJWSK6VOKS3PO5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MSBYOQ7LIME6OJWSK6VOKS3PO5/action/storage_attestation","attest_author":"https://pith.science/pith/MSBYOQ7LIME6OJWSK6VOKS3PO5/action/author_attestation","sign_citation":"https://pith.science/pith/MSBYOQ7LIME6OJWSK6VOKS3PO5/action/citation_signature","submit_replication":"https://pith.science/pith/MSBYOQ7LIME6OJWSK6VOKS3PO5/action/replication_record"}},"created_at":"2026-07-04T14:40:03.529223+00:00","updated_at":"2026-07-04T14:40:03.529223+00:00"}