Indecomposable modules of the intermediate series over W(a,b) algebras

2011/03/20 by Yucai Su, Ying Xu, Su, Yucai +3
Mathematics · Physics and Astronomy · #17B10 #17B68 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1103.3850

openalex publication_date 2011/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any complex parameters a,b, the W(a,b) algebra is the Lie algebra with basis L_i,W_i|i∈ Z, and relations [L_i,L_j]=(j-i)L_i+j, [L_i,W_j]=(a+j+bi)W_i+j,[W_i,W_j]=0. In this paper, indecomposable modules of the intermediate series over W(a,b) are classified. It is also proved that an irreducible Harish-Chandra W(a,b)-module is either a highest/lowest weight module or a uniformly bounded module. Furthermore, if a∉ Q, an irreducible weight W(a,b)-module is simply a Vir-module with trivial actions of W_k.

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