{"paper":{"title":"Quasifinite representations of a class of Block type Lie algebras $\\BB$","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":"2011-02-25T08:16:59Z","abstract_excerpt":"Intrigued by a well-known theorem of Mathieu's on Harish-Chandra modules over the Virasoro algebra, we give an analogous result for a class of Block type Lie algebras $\\BB$, where the parameter $q$ is a nonzero complex number. We also classify quasifinite irreducible highest weight $\\BB$-modules and irreducible $\\BB$-modules of the intermediate series. In particular, we obtain that an irreducible $\\BB$-module of the intermediate series may be a nontrivial extension of a $\\Vir$-module of the intermediate series if $q$ is half of a negative integer, where $\\Vir$ is a subalgebra of $\\BB$ isomorph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5187","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"}