3-李代数A_(w)^(δ)的模与诱导模

Modules and induced modules of 3-Lie algebra A_(w)^(δ)

对特征零域F上无限维单3-李代数A_(w)^(δ),构造了两类A_(w)^(δ)的无限维中间序列模(V,ρλ,0)=Tλ,0与(V,ρλ,1)=T_(λ,1)和一类无限维ad(A__(w)^(δ))-模(V,ψ_(λ,μ)),其中λ,μ∈F,并对3-李代数A_(w)^(δ)-模与诱导模之间的关系进行了研究.证明了只有两类无限维模(V,ψ_(λ,1))和(V,ψ_(λ,0))是诱导模.

For the infinite dimensional simple 3-Lie algebra A_(w)^(δ)over a field F of characteristic zero,we construct two infinite dimensional intermediate series modules(V,ρλ,0)=Tλ,0 and(V,ρ_(λ,1))=Tλ,1 of A_(w)^(δ)as well as a class of infinite dimensional modules(V,ψλ,μ)of ad(A_(w)^(δ)),whereλ,μ∈F.The relation between3-Lie algebra A_(w)^(δ)-modules and induced modules of ad(A_(w)^(δ))are discussed.It is shown that only two of infinite dimensional modules,namely(V,ψ_(λ,1))and(V,ψ_(λ,0)),are induced modules.