{"paper":{"title":"Block type Lie algebras and their representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Shasha Zhao, Xiaomin Tang","submitted_at":"2016-11-06T07:31:00Z","abstract_excerpt":"Block type Lie algebras have been studied by many authors in the latest twenty years. In this paper, we will study a class of more general Block type Lie algebra $\\mathcal{B}(p,q)$, which is a class of infinite-dimensional Lie algebra by using the generalized Balinskii-Novikov's construction method to Witt type Novikov algebra. We study the representation theory for $\\mathcal{B}(p,q)$. We classify quasifinite irreducible highest weight $\\mathcal{B}(p,q)$-module. We also prove that any quasifinite irreducible module of Block type Lie algebras $\\mathcal{B}(p,q)$ is either a highest or lowest wei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01736","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"}