对特征零域 $\mathbb F$ 上无限维单 $3$ -李代数 $A_{\omega}^{\delta}$ , 构造了两类 $A_{\omega}^{\delta}$ 的无限维中间序列模 $(V, \rho_{\lambda, 0})=T_{\lambda, 0}$ 与 $(V, \rho_{\lambda, 1})=T_{\lambda, 1}$ 和一类无限维ad $(A_{\omega}^{\delta})$ -模 $(V, \psi_{\lambda,\mu})$ , 其中 $\lambda, \mu\in \mathbb F$ , 并对3-李代数 $A_{\omega}^{\delta}$ -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 $(V, \psi_{\lambda,1})$ 和 $(V, \psi_{\lambda, 0})$ 是诱导模.

For the infinite dimensional simple 3-Lie algebra $A_{\omega}^{\delta}$ over a field $\mathbb F$ of characteristic zero, we construct two infinite dimensional intermediate series modules $(V, \rho_{\lambda, 0})=T_{\lambda, 0}$ and $(V, \rho_{\lambda, 1})=T_{\lambda, 1}$ of $A_{\omega}^{\delta}$ as well as a class of infinite dimensional modules $(V, \psi_{\lambda,\mu})$ of ad $(A_{\omega}^{\delta})$ , where $\lambda, \mu\in \mathbb F$ . The relation between 3-Lie algebra $A_{\omega}^{\delta}$ -modules and induced modules of ad $(A_{\omega}^{\delta})$ are discussed. It is shown that only two of infinite dimensional modules, namely $(V, \psi_{\lambda, 1})$ and $(V, \psi_{\lambda, 0})$ , are induced modules.