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Then we determine extensions between two finite irreducible conformal $\\mathcal{R}$-modules."},"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":"1907.02960","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-07-03T03:58:16Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4d8d4dbbb9790356f99d6c25ac5c03c900d8c70340fede990b3aa9eeca0b8b18","abstract_canon_sha256":"4a8c9cbf059ec1f2279fbb00f023dda670cbd9eb6f6f832e8e04efa5a03651ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:22.529304Z","signature_b64":"CD/UMFpbjdko33VYkk9FcAIsTgWapl6HAjRkK3noxT+Wa46YgobHvRxonaZ0kHdjKU2L/Bqd/FpqMvNDlhaUAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c5209d4918e8d1b08f5e529b0ac666344c75da4f3166051947e94d0e843b075","last_reissued_at":"2026-05-17T23:41:22.528727Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:22.528727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conformal modules and their extensions of a Lie conformal algebra related to a 2-dimensional Novikov algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RT","authors_text":"Lamei Yuan, Yanjie Wang","submitted_at":"2019-07-03T03:58:16Z","abstract_excerpt":"Let $\\mathcal{R}$ be a free Lie conformal algebra of rank $2$ with $\\mathbb{C}[\\partial]$-basis $\\{L,I\\}$ and relations \\begin{eqnarray*} \\left[L_{\\lambda} L\\right]=(\\partial+2 \\lambda) (L+I),\\ \\left[L_{\\lambda} I\\right]=(\\partial+\\lambda) I, \\ \\left[I_{\\lambda} L\\right]=\\lambda I,\\ \\left[I_{\\lambda} I\\right]=0. \\end{eqnarray*} In this paper, we first classify all finite nontrivial irreducible conformal modules over $\\mathcal{R}$. 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