Abstract:

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.

Key words: 3-Lie algebra-module, induced module, intermediate series module