Quasifinite representations of a class of Block type Lie algebras \BB

2011/02/25 by Yucai Su, Su, Yucai, Chunguang Xia +3
Mathematics · Physics and Astronomy · #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.1102.5187

openalex publication_date 2011/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 isomorphic to the Virasoro algebra.

Related

• Classification of quasifinite representations of a Lie algebra related to Block type
• Block type Lie algebras and their representations
• Verma modules over a Block Lie algebra
• Highest weight representations of a Lie algebra of Block type
• Harish-Chandra modules over the \Q Heisenberg-Virasoro Algebra