{"paper":{"title":"Loop W(a,b) Lie conformal algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Bo Yu, Guangzhe Fan, Henan Wu","submitted_at":"2016-03-01T05:27:49Z","abstract_excerpt":"Fix $a,b\\in\\C$, let $LW(a,b)$ be the loop $W(a,b)$ Lie algebra over $\\C$ with basis $\\{L_{\\a,i},I_{\\b,j} \\mid \\a,\\b,i,j\\in\\Z\\}$ and relations $[L_{\\a,i},L_{\\b,j}]=(\\a-\\b)L_{\\a+\\b,i+j}, [L_{\\a,i},I_{\\b,j}]=-(a+b\\a+\\b)I_{\\a+\\b,i+j},[I_{\\a,i},I_{\\b,j}]=0$, where $\\a,\\b,i,j\\in\\Z$. In this paper, a formal distribution Lie algebra of $LW(a,b)$ is constructed. Then the associated conformal algebra $CLW(a,b)$ is studied, where $CLW(a,b)$ has a $\\C[\\partial]$-basis $\\{L_i,I_j\\,|\\,i,j\\in\\Z\\}$ with $\\lambda$-brackets $[L_i\\, {}_\\lambda \\, L_j]=(\\partial+2\\lambda) L_{i+j}, [L_i\\, {}_\\lambda \\, I_j]=(\\part"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00147","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":""},"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"}