华东师范大学学报（自然科学版） ›› 2021, Vol. 2021 ›› Issue (3): 8-16.doi: 10.3969/j.issn.1000-5641.2021.03.002

• • 上一篇    下一篇

3-李代数Aω δ的模与诱导模

白瑞蒲1,2(), 马越1,2   

  1. 1. 河北大学 数学与信息科学学院, 河北 保定　071002
    2. 河北省机器学习与智能计算重点实验室, 河北 保定　071002
  • 收稿日期:2020-02-18 出版日期:2021-05-25 发布日期:2021-05-26

Modules and induced modules of 3-Lie algebra Aω δ

Ruipu BAI1,2(), Yue MA1,2   

  1. 1. College of Mathematics and Information Science, Hebei University, Baoding Hebei　071002, China
    2. Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province, Baoding Hebei　071002, China
  • Received:2020-02-18 Online:2021-05-25 Published:2021-05-26

RichHTML

1418

PDF

155

摘要：

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.

关键词: 3-李代数-模, 诱导模, 中间序列模

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

中图分类号: