{"paper":{"title":"Classification of quasifinite representations of a Lie algebra related to Block type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Chunguang Xia, Ying Xu, Yucai Su","submitted_at":"2012-10-26T13:08:18Z","abstract_excerpt":"A well-known theorem of Mathieu's states that a Harish-chandra module over the Virasoro algebra is either a highest weight module, a lowest weight module or a module of the intermediate series. It is proved in this paper that an analogous result also holds for the Lie algebra $\\BB$ related to Block type, with basis {L_{\\a,i},C|a,i\\in\\Z, i\\ge0} and relations [L_{\\a,i},L_{\\b,j}]=((i+1)\\b-(j+1)\\a)L_{\\a+\\b,i+j}+\\d_{\\a+\\b,0}\\d_{i+j,0}\\frac{\\a^3-\\a}{6}C, [C,L_{\\a,i}]=0.Namely, an irreducible quasifinite $\\BB$-module is either a highest weight module, a lowest weight module or a module of the interme"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7132","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"}