Verma modules over a Block Lie algebra

2005/12/15 by Qifeng Jiang, Qifen Jiang, Jiang, Qifen +2
Mathematics · Physics and Astronomy · #17B10 #17B65 #17B68 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B10 #msc:17B65 #msc:17B68

paper · pdf · doi:10.48550/arxiv.math/0512351

7 pages. The previous version was posted by a mistake

openalex publication_date 2005/12/15 · arxiv created 2006/02/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let B be the Lie algebra with basis L_i,j,C|i,j∈ Z and relations [L_i,j,L_k,l]=((j+1)k-i(l+1))L_i+k,j+l+iδ_i,-kδ_j+l,-2C, [C,L_i,j]=0. It is proved that an irreducible highest weight B-module is quasifinite if and only if it is a proper quotient of a Verma module. For an additive subgroup G of the base field F, there corresponds to a Lie algebra B(G) of Block type. Given a totalorder \succ on G and a weight Λ, a Verma B(G)-module M(Λ,\succ) is defined. The irreducibility of M(Λ,\succ) is completely determined.

Related

• Highest weight representations of a Lie algebra of Block type
• Verma modules over a class of Block type Lie algebras
• Classification of quasifinite representations of a Lie algebra related to Block type
• Quasifinite representations of a class of Block type Lie algebras \BB
• Block type Lie algebras and their representations