Classification of quasifinite representations of a Lie algebra related to Block type

2012/10/26 by Yucai Su, Su, Yucai, Chunguang Xia +3 · 2 citations
Mathematics · #17B10 #17B65 #17B68 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1210.7132

openalex publication_date 2012/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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∈\Z, i≥0 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(\a³-\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 intermediate series.

Cited by

• Non-weight modules over generalized Heisenberg-Virasoro algebra of rank two
• Non-weight modules over gap-p Virasoro algebras

Related

• Quasifinite representations of a class of Block type Lie algebras \BB
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• Highest weight representations of a Lie algebra of Block type
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