3-Lie algebra A_ω^δ-modules and induced modules

2019/04/25 by Ruipu Bai, Yue Ma, Bai, Ruipu +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1904.11196

openalex publication_date 2019/04/25 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In this paper, we define the induced modules of Lie algebra ad(B) associated with a 3-Lie algebra B-module, and study the relation between 3-Lie algebra A_ω^δ-modules and induced modules of inner derivation algebra ad(A_ω^δ). We construct two infinite dimensional intermediate series modules of 3-Lie algebra A_ω^δ, and two infinite dimensional modules (V, ψ_λμ) and (V, ϕ_μ) of the Lie algebra ad(A_ω^δ), and prove that only (V, ψ_λ0) and (V, ψ_λ1) are induced modules.

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