{"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 $\\mathcal{R}$. Then we determine extensions between two finite irreducible conformal $\\mathcal{R}$-modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02960","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":""},"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"}