Non-weight modules over generalized Heisenberg-Virasoro algebra of rank two

2025/12/08 by Wen, Yi, Jing, Naihuan, Sun, Jiancai +1
Mathematics · #17B05 #17B40 #17B68 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2512.07254

openalex publication_date 2025/12/08 · openalex created_date 2025/12/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study a class of non-weight modules over the generalized Heisenberg-Virasoro algebra of rank two \widetildeL(p₁, p₂). We construct a family of irreducible \widetildeL(p₁, p₂)-modules, determine the isomorphism classes and show that these modules exhaust all the \widetildeL(p₁, p₂)-modules that are free modules of rank one over the Cartan subalgebra.

Citations

• On non-weight representations of the N = 2 superconformal algebras
• Non-weight representations of Cartan type S Lie algebras
• Non-weight representations of Cartan type S Lie algebras
• Classification of quasifinite representations of a Lie algebra related to Block type

Related

• Representations of the N=1 Heisenberg-Virasoro superalgebra
• Non-weight modules over algebras related to the 2d supersymmetric Galilean conformal algebra
• A class of non-weight modules over the Schrödinger-Virasoro algebras
• Non-weight modules over a Schrödinger-Virasoro type algebra
• Representations of non-finitely graded Heisenberg-Virasoro type Lie algebras